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<div id="org-div-home-and-up">
<a accesskey="h" href=""> UP </a>
|
<a accesskey="H" href="index.html"> HOME </a>
</div><div id="content">
<h1 class="title">Common</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org57d1cb3">1. Angular Momentum</a>
<ul>
<li><a href="#orge0c61ad">1.1. Type</a></li>
<li><a href="#orgd6ebc87">1.2. Conversions</a></li>
<li><a href="#org1e7baad">1.3. Shell functions</a></li>
<li><a href="#org3aada94">1.4. Arithmetic</a></li>
<li><a href="#org0cc7d45">1.5. Printers</a></li>
<li><a href="#org87e49fd">1.6. <span class="todo TODO">TODO</span> Tests</a></li>
</ul>
</li>
<li><a href="#org711e55a">2. Bit string</a>
<ul>
<li><a href="#orgbf2cfca">2.1. Type</a></li>
<li><a href="#orgbb9eae5">2.2. General implementation</a></li>
<li><a href="#org06c6762">2.3. Printers</a></li>
</ul>
</li>
<li><a href="#org24486dc">3. Charge</a>
<ul>
<li><a href="#orgd2115aa">3.1. Type</a></li>
<li><a href="#org0f3bf24">3.2. Conversions</a></li>
<li><a href="#org5171c3e">3.3. Simple operations</a></li>
<li><a href="#org4755a94">3.4. Printers</a></li>
</ul>
</li>
<li><a href="#org6d00d5f">4. Command line</a>
<ul>
<li><a href="#orgf56b3ee">4.1. Type</a></li>
<li><a href="#orgd87f5ce">4.2. Mutable attributes</a></li>
<li><a href="#org2aa0f74">4.3. Query functions</a></li>
<li><a href="#org6289fa0">4.4. Specification</a></li>
</ul>
</li>
<li><a href="#orgf025e44">5. Constants</a>
<ul>
<li><a href="#org54df39c">5.1. Thresholds</a></li>
<li><a href="#org7754673">5.2. Mathematical constants</a></li>
<li><a href="#org4a6d922">5.3. Physical constants</a></li>
</ul>
</li>
<li><a href="#org12d227a">6. Coordinate</a>
<ul>
<li><a href="#org62fcc02">6.1. Type</a></li>
<li><a href="#orga380f75">6.2. Creation</a></li>
<li><a href="#org7f6d675">6.3. Conversion</a></li>
<li><a href="#org925ab51">6.4. Vector operations</a></li>
<li><a href="#orgc043b39">6.5. Printers</a></li>
</ul>
</li>
<li><a href="#org1923bd8">7. Non-negative float</a>
<ul>
<li><a href="#orgbcd34bb">7.1. Type</a></li>
<li><a href="#orgbe46fd2">7.2. Conversions</a></li>
</ul>
</li>
<li><a href="#org8d1e251">8. Powers</a>
<ul>
<li><a href="#org2427f71">8.1. Type</a></li>
<li><a href="#orgcb55052">8.2. Conversions</a></li>
<li><a href="#org744d5ef">8.3. Operations</a></li>
<li><a href="#orgd52d720">8.4. Printers</a></li>
</ul>
</li>
<li><a href="#org012eacd">9. QCaml</a></li>
<li><a href="#orgba955b4">10. Range</a>
<ul>
<li><a href="#orgc921ed3">10.1. Type</a></li>
<li><a href="#orga7b85a3">10.2. Conversion</a></li>
<li><a href="#org92dc675">10.3. Printers</a></li>
</ul>
</li>
<li><a href="#orgc8e5623">11. Spin</a>
<ul>
<li><a href="#orge61ea06">11.1. Type</a></li>
<li><a href="#orgb870fcb">11.2. Functions</a></li>
<li><a href="#orgd0f4806">11.3. Printers</a></li>
</ul>
</li>
<li><a href="#org30d2221">12. Util</a>
<ul>
<li><a href="#orgba158b9">12.1. External C functions</a>
<ul>
<li><a href="#org5a22bbb">12.1.1. Erf</a></li>
<li><a href="#org3e8d069">12.1.2. Erfc</a></li>
<li><a href="#orgb4df3c2">12.1.3. Gamma</a></li>
<li><a href="#org6c5d330">12.1.4. Popcnt</a></li>
<li><a href="#orgdfb5f51">12.1.5. Trailz</a></li>
<li><a href="#org3eb911e">12.1.6. Leadz</a></li>
<li><a href="#org2d822a2">12.1.7. Test</a></li>
</ul>
</li>
<li><a href="#org8e236a2">12.2. General functions</a></li>
<li><a href="#org129b6ff">12.3. Functions related to the Boys function</a></li>
<li><a href="#org0b6cdc7">12.4. List functions</a></li>
<li><a href="#org91499d0">12.5. Array functions</a></li>
<li><a href="#org96db98c">12.6. Stream functions</a></li>
<li><a href="#orgbf0f986">12.7. Printers</a></li>
</ul>
</li>
<li><a href="#org912d5d1">13. Zkey</a>
<ul>
<li><a href="#org001f90b">13.1. Types</a></li>
<li><a href="#org9ac062e">13.2. Conversions</a></li>
<li><a href="#org6f8b1b7">13.3. Functions for hash tables</a></li>
<li><a href="#org0d32047">13.4. Printers</a></li>
</ul>
</li>
<li><a href="#org39b0e68">14. Zmap</a>
<ul>
<li><a href="#org43d8800">14.1. Type</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div class="org-src-container">
<pre class="src src-ocaml" id="orgee95983"><span class="org-string">"Utility functions used by all the other directories."</span>
</pre>
</div>
<div id="outline-container-org57d1cb3" class="outline-2">
<h2 id="org57d1cb3"><span class="section-number-2">1</span> Angular Momentum</h2>
<div class="outline-text-2" id="text-1">
<p>
Azimuthal quantum number, repsesented as \( s,p,d,\dots \) .
</p>
</div>
<div id="outline-container-orge0c61ad" class="outline-3">
<h3 id="orge0c61ad"><span class="section-number-3">1.1</span> Type</h3>
<div class="outline-text-3" id="text-1-1">
<div class="org-src-container">
<pre class="src src-ocaml" id="orge349bb8"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span> <span class="org-tuareg-font-lock-operator">=</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">S</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">P</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">D</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">F</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">G</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">H</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">I</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">J</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">K</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">L</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">M</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">N</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">O</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Int</span> <span class="org-keyword">of</span> int
<span class="org-keyword">exception</span> <span class="org-tuareg-font-lock-constructor">Angular_momentum_error</span> <span class="org-keyword">of</span> string
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">kind</span> <span class="org-tuareg-font-lock-operator">=</span>
<span class="org-tuareg-font-lock-constructor">Singlet</span> <span class="org-keyword">of</span> t
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Doublet</span> <span class="org-keyword">of</span> <span class="org-tuareg-font-lock-operator">(</span>t <span class="org-tuareg-font-lock-operator">*</span> t<span class="org-tuareg-font-lock-operator">)</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Triplet</span> <span class="org-keyword">of</span> <span class="org-tuareg-font-lock-operator">(</span>t <span class="org-tuareg-font-lock-operator">*</span> t <span class="org-tuareg-font-lock-operator">*</span> t<span class="org-tuareg-font-lock-operator">)</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Quartet</span> <span class="org-keyword">of</span> <span class="org-tuareg-font-lock-operator">(</span>t <span class="org-tuareg-font-lock-operator">*</span> t <span class="org-tuareg-font-lock-operator">*</span> t <span class="org-tuareg-font-lock-operator">*</span> t<span class="org-tuareg-font-lock-operator">)</span>
</pre>
</div>
<p>
An exception is raised when the <code>Angular_momentum.t</code> element can't
be created.
</p>
<p>
The <code>kind</code> is used to build shells, shell doublets, triplets or
quartets, use in the two-electron operators.
</p>
</div>
</div>
<div id="outline-container-orgd6ebc87" class="outline-3">
<h3 id="orgd6ebc87"><span class="section-number-3">1.2</span> Conversions</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_char</span> <span class="org-tuareg-font-lock-operator">:</span> char <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_char</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> char
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_int</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_int</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_string</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> string
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>of_char</code></td>
<td class="org-left">Returns an <code>Angular_momentum.t</code> when a shell is given as a character (case insensitive)</td>
</tr>
<tr>
<td class="org-left"><code>to_char</code></td>
<td class="org-left">Converts the angular momentum into a char</td>
</tr>
<tr>
<td class="org-left"><code>of_int</code></td>
<td class="org-left">Returns a shell given an \(l\) value.</td>
</tr>
<tr>
<td class="org-left"><code>to_int</code></td>
<td class="org-left">Returns the \(l_{max}\) value of the shell</td>
</tr>
<tr>
<td class="org-left"><code>to_string</code></td>
<td class="org-left">Converts the angular momentum into a string</td>
</tr>
</tbody>
</table>
<pre class="example" id="orgd0d73bd">
Angular_momentum.of_char 'p';;
- : Angular_momentum.t = P
Angular_momentum.(to_char P);;
- : char = 'P'
Angular_momentum.of_int 2;;
- : Angular_momentum.t = D
Angular_momentum.(to_int D);;
- : int = 2
Angular_momentum.(to_string D);;
- : string = "D"
</pre>
</div>
</div>
<div id="outline-container-org1e7baad" class="outline-3">
<h3 id="org1e7baad"><span class="section-number-3">1.3</span> Shell functions</h3>
<div class="outline-text-3" id="text-1-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">n_functions</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">zkey_array</span> <span class="org-tuareg-font-lock-operator">:</span> kind <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Zkey.</span>t array
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>n_functions</code></td>
<td class="org-left">Returns the number of cartesian functions in a shell.</td>
</tr>
<tr>
<td class="org-left"><code>zkey_array</code></td>
<td class="org-left">Array of <code>Zkey.t</code>, where each element is a a key associated with the the powers of \(x,y,z\).</td>
</tr>
</tbody>
</table>
<pre class="example" id="org1451778">
Angular_momentum.(n_functions D) ;;
- : int = 6
Angular_momentum.( zkey_array (Doublet (P,S)) );;
- : Zkey.t array =
[|&lt; 01125899906842624 | 1, 0, 0, 0, 0, 0 &gt;;
&lt; 01099511627776 | 0, 1, 0, 0, 0, 0 &gt;;
&lt; 01073741824 | 0, 0, 1, 0, 0, 0 &gt;|]
</pre>
</div>
</div>
<div id="outline-container-org3aada94" class="outline-3">
<h3 id="org3aada94"><span class="section-number-3">1.4</span> Arithmetic</h3>
<div class="outline-text-3" id="text-1-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-tuareg-font-lock-operator">(</span> <span class="org-tuareg-font-lock-operator">+</span> <span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-tuareg-font-lock-operator">(</span> <span class="org-tuareg-font-lock-operator">-</span> <span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
</pre>
</div>
<pre class="example" id="orgf06f93d">
Angular_momentum.(D + P);;
- : Angular_momentum.t = F
Angular_momentum.(F - P);;
- : Angular_momentum.t = D
</pre>
</div>
</div>
<div id="outline-container-org0cc7d45" class="outline-3">
<h3 id="org0cc7d45"><span class="section-number-3">1.5</span> Printers</h3>
<div class="outline-text-3" id="text-1-5">
<p>
Printers can print as a string (default) or as an integer.
</p>
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp_string</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp_int</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
</div>
</div>
<div id="outline-container-org87e49fd" class="outline-3">
<h3 id="org87e49fd"><span class="section-number-3">1.6</span> <span class="todo TODO">TODO</span> Tests</h3>
</div>
</div>
<div id="outline-container-org711e55a" class="outline-2">
<h2 id="org711e55a"><span class="section-number-2">2</span> Bit string</h2>
<div class="outline-text-2" id="text-2">
<p>
We define here a data type to handle bit strings efficiently. When
the bit string contains less than 64 bits, it is stored internally
in a 63-bit integer and uses bitwise instructions. When more than
63 bits are required, the <code>zarith</code> library is used to consider the
bit string as a multi-precision integer.
</p>
</div>
<div id="outline-container-orgbf2cfca" class="outline-3">
<h3 id="orgbf2cfca"><span class="section-number-3">2.1</span> Type</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgbb9eae5" class="outline-3">
<h3 id="orgbb9eae5"><span class="section-number-3">2.2</span> General implementation</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_int</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_z</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Z.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">zero</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">is_zero</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> bool
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">numbits</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">testbit</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> bool
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">neg</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">shift_left</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">shift_right</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">shift_left_one</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">logor</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">logxor</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">logand</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">lognot</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">plus_one</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">minus_one</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">hamdist</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">trailing_zeros</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">popcount</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_list</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-label">?accu</span><span class="org-tuareg-font-lock-operator">:(</span>int list<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int list
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">permutations</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t list
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>of_int</code></td>
<td class="org-left">Creates a bit string from an <code>int</code></td>
</tr>
<tr>
<td class="org-left"><code>of_z</code></td>
<td class="org-left">Creates a bit string from an <code>Z.t</code> multi-precision integer</td>
</tr>
<tr>
<td class="org-left"><code>zero</code></td>
<td class="org-left"><code>zero n</code> creates a zero bit string with <code>n</code> bits</td>
</tr>
<tr>
<td class="org-left"><code>is_zero</code></td>
<td class="org-left">True if all the bits of the bit string are zero.</td>
</tr>
<tr>
<td class="org-left"><code>numbits</code></td>
<td class="org-left">Returns the number of bits used to represent the bit string</td>
</tr>
<tr>
<td class="org-left"><code>testbit</code></td>
<td class="org-left"><code>testbit t n</code> is true if the <code>n</code>-th bit of the bit string <code>t</code> is set to <code>1</code></td>
</tr>
<tr>
<td class="org-left"><code>neg</code></td>
<td class="org-left">Returns the negative of the integer interpretation of the bit string</td>
</tr>
<tr>
<td class="org-left"><code>shift_left</code></td>
<td class="org-left"><code>shift_left t n</code> returns a new bit strings with all the bits shifted <code>n</code> positions to the left</td>
</tr>
<tr>
<td class="org-left"><code>shift_right</code></td>
<td class="org-left"><code>shift_right t n</code> returns a new bit strings with all the bits shifted <code>n</code> positions to the right</td>
</tr>
<tr>
<td class="org-left"><code>shift_left_one</code></td>
<td class="org-left"><code>shift_left_one size n</code> returns a new bit strings with the <code>n</code>-th bit set to one. It is equivalent as shifting <code>1</code> by <code>n</code> bits to the left, <code>size</code> is the total number of bits of the bit string</td>
</tr>
<tr>
<td class="org-left"><code>logor</code></td>
<td class="org-left">Bitwise logical or</td>
</tr>
<tr>
<td class="org-left"><code>logxor</code></td>
<td class="org-left">Bitwise logical exclusive or</td>
</tr>
<tr>
<td class="org-left"><code>logand</code></td>
<td class="org-left">Bitwise logical and</td>
</tr>
<tr>
<td class="org-left"><code>lognot</code></td>
<td class="org-left">Bitwise logical negation</td>
</tr>
<tr>
<td class="org-left"><code>plus_one</code></td>
<td class="org-left">Takes the integer representation of the bit string and adds one</td>
</tr>
<tr>
<td class="org-left"><code>minus_one</code></td>
<td class="org-left">Takes the integer representation of the bit string and removes one</td>
</tr>
<tr>
<td class="org-left"><code>hamdist</code></td>
<td class="org-left">Returns the Hamming distance, i.e. the number of bits differing between two bit strings</td>
</tr>
<tr>
<td class="org-left"><code>trailing_zeros</code></td>
<td class="org-left">Returns the number of trailing zeros in the bit string</td>
</tr>
<tr>
<td class="org-left"><code>permutations</code></td>
<td class="org-left"><code>permutations m n</code> generates the list of all possible <code>n</code>-bit strings with <code>m</code> bits set to <code>1</code>. Algorithm adapted from <a href="https://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation">Bit twiddling hacks</a></td>
</tr>
<tr>
<td class="org-left"><code>popcount</code></td>
<td class="org-left">Returns the number of bits set to one in the bit string</td>
</tr>
<tr>
<td class="org-left"><code>to_list</code></td>
<td class="org-left">Converts a bit string into a list of integers indicating the positions where the bits are set to <code>1</code>. The first value for the position is not <code>0</code> but <code>1</code></td>
</tr>
</tbody>
</table>
<pre class="example" id="orge3bc8cc">
Bitstring.of_int 15;;
- : Bitstring.t =
++++------------------------------------------------------------
</pre>
<pre class="example" id="org21a8f00">
Bitstring.(shift_left (of_int 15) 2);;
- : Bitstring.t =
--++++----------------------------------------------------------
Bitstring.(shift_right (of_int 15) 2);;
- : Bitstring.t =
++--------------------------------------------------------------
Bitstring.shift_left_one 32 4;;
- : Bitstring.t =
----+-----------------------------------------------------------
Bitstring.(testbit (of_int 15) 3);;
- : bool = true
Bitstring.(testbit (of_int 15) 4);;
- : bool = false
</pre>
<pre class="example" id="orgb855bff">
Bitstring.(logor (of_int 15) (of_int 73));;
- : Bitstring.t =
++++--+---------------------------------------------------------
Bitstring.(logand (of_int 15) (of_int 10));;
- : Bitstring.t =
-+-+------------------------------------------------------------
Bitstring.(logxor (of_int 15) (of_int 73));;
- : Bitstring.t =
-++---+---------------------------------------------------------
</pre>
<pre class="example" id="orgbade43c">
Bitstring.(plus_one (of_int 15));;
- : Bitstring.t =
----+-----------------------------------------------------------
Bitstring.(minus_one (of_int 15));;
- : Bitstring.t =
-+++------------------------------------------------------------
</pre>
<pre class="example" id="org2b53e4a">
Bitstring.(trailing_zeros (of_int 12));;
- : int = 2
Bitstring.(hamdist (of_int 15) (of_int 73));;
- : int = 3
Bitstring.(popcount (of_int 15));;
- : int = 4
</pre>
<pre class="example" id="orgdd8c928">
Bitstring.(to_list (of_int 45));;
- : int list = [1; 3; 4; 6]
</pre>
<pre class="example" id="orgc8dbb88">
Bitstring.permutations 2 4;;
- : Bitstring.t list =
[++--------------------------------------------------------------;
+-+-------------------------------------------------------------;
-++-------------------------------------------------------------;
+--+------------------------------------------------------------;
-+-+------------------------------------------------------------;
--++------------------------------------------------------------]
</pre>
</div>
</div>
<div id="outline-container-org06c6762" class="outline-3">
<h3 id="org06c6762"><span class="section-number-3">2.3</span> Printers</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org24486dc" class="outline-2">
<h2 id="org24486dc"><span class="section-number-2">3</span> Charge</h2>
<div class="outline-text-2" id="text-3">
</div>
<div id="outline-container-orgd2115aa" class="outline-3">
<h3 id="orgd2115aa"><span class="section-number-3">3.1</span> Type</h3>
<div class="outline-text-3" id="text-3-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span>
</pre>
</div>
<p>
This type should be used for all charges in the program (electrons, nuclei,&#x2026;).
</p>
</div>
</div>
<div id="outline-container-org0f3bf24" class="outline-3">
<h3 id="org0f3bf24"><span class="section-number-3">3.2</span> Conversions</h3>
<div class="outline-text-3" id="text-3-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_float</span> <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_float</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_int</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_int</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_string</span><span class="org-tuareg-font-lock-operator">:</span> string <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_string</span><span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> string
</pre>
</div>
</div>
</div>
<div id="outline-container-org5171c3e" class="outline-3">
<h3 id="org5171c3e"><span class="section-number-3">3.3</span> Simple operations</h3>
<div class="outline-text-3" id="text-3-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-tuareg-font-lock-operator">(</span> <span class="org-tuareg-font-lock-operator">+</span> <span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-tuareg-font-lock-operator">(</span> <span class="org-tuareg-font-lock-operator">-</span> <span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-tuareg-font-lock-operator">(</span> <span class="org-tuareg-font-lock-operator">*</span> <span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-tuareg-font-lock-operator">(</span> <span class="org-tuareg-font-lock-operator">/</span> <span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">is_null</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> bool
</pre>
</div>
</div>
</div>
<div id="outline-container-org4755a94" class="outline-3">
<h3 id="org4755a94"><span class="section-number-3">3.4</span> Printers</h3>
<div class="outline-text-3" id="text-3-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org6d00d5f" class="outline-2">
<h2 id="org6d00d5f"><span class="section-number-2">4</span> Command line</h2>
<div class="outline-text-2" id="text-4">
<p>
This module is a wrapper around the <code>Getopt</code> library and helps to
define command-line arguments.
</p>
<p>
Here is an example of how to use this module.
First, define the specification:
</p>
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">let</span> <span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Command_line</span> <span class="org-tuareg-font-lock-governing">in</span>
<span class="org-tuareg-font-lock-governing">begin</span>
set_header_doc <span class="org-tuareg-font-lock-operator">(</span><span class="org-tuareg-font-lock-module">Sys.</span>argv.<span class="org-tuareg-font-lock-operator">(</span>0<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">^</span> <span class="org-string">" - One-line description"</span><span class="org-tuareg-font-lock-operator">);</span>
set_description_doc <span class="org-string">"Long description of the command."</span><span class="org-tuareg-font-lock-operator">;</span>
set_specs
<span class="org-tuareg-font-lock-operator">[</span> <span class="org-tuareg-font-lock-operator">{</span> short<span class="org-tuareg-font-lock-operator">=</span><span class="org-string">'c'</span><span class="org-tuareg-font-lock-operator">;</span> long<span class="org-tuareg-font-lock-operator">=</span><span class="org-string">"check"</span><span class="org-tuareg-font-lock-operator">;</span> opt<span class="org-tuareg-font-lock-operator">=</span><span class="org-tuareg-font-lock-constructor">Optional</span><span class="org-tuareg-font-lock-operator">;</span>
doc<span class="org-tuareg-font-lock-operator">=</span><span class="org-string">"Checks the input data"</span><span class="org-tuareg-font-lock-operator">;</span>
arg<span class="org-tuareg-font-lock-operator">=</span><span class="org-tuareg-font-lock-constructor">Without_arg</span><span class="org-tuareg-font-lock-operator">;</span> <span class="org-tuareg-font-lock-operator">};</span>
<span class="org-tuareg-font-lock-operator">{</span> short<span class="org-tuareg-font-lock-operator">=</span><span class="org-string">'b'</span> <span class="org-tuareg-font-lock-operator">;</span> long<span class="org-tuareg-font-lock-operator">=</span><span class="org-string">"basis"</span> <span class="org-tuareg-font-lock-operator">;</span> opt<span class="org-tuareg-font-lock-operator">=</span><span class="org-tuareg-font-lock-constructor">Mandatory</span><span class="org-tuareg-font-lock-operator">;</span>
arg<span class="org-tuareg-font-lock-operator">=</span><span class="org-tuareg-font-lock-constructor">With_arg</span> <span class="org-string">"&lt;string&gt;"</span><span class="org-tuareg-font-lock-operator">;</span>
doc<span class="org-tuareg-font-lock-operator">=</span><span class="org-string">"Name of the file containing the basis set"</span><span class="org-tuareg-font-lock-operator">;</span> <span class="org-tuareg-font-lock-operator">}</span> <span class="org-tuareg-font-lock-operator">;</span>
<span class="org-tuareg-font-lock-operator">{</span> short<span class="org-tuareg-font-lock-operator">=</span><span class="org-string">'m'</span> <span class="org-tuareg-font-lock-operator">;</span> long<span class="org-tuareg-font-lock-operator">=</span><span class="org-string">"multiplicity"</span> <span class="org-tuareg-font-lock-operator">;</span> opt<span class="org-tuareg-font-lock-operator">=</span><span class="org-tuareg-font-lock-constructor">Optional</span><span class="org-tuareg-font-lock-operator">;</span>
arg<span class="org-tuareg-font-lock-operator">=</span><span class="org-tuareg-font-lock-constructor">With_arg</span> <span class="org-string">"&lt;int&gt;"</span><span class="org-tuareg-font-lock-operator">;</span>
doc<span class="org-tuareg-font-lock-operator">=</span><span class="org-string">"Spin multiplicity (2S+1). Default is singlet"</span><span class="org-tuareg-font-lock-operator">;</span> <span class="org-tuareg-font-lock-operator">}</span> <span class="org-tuareg-font-lock-operator">;</span>
<span class="org-tuareg-font-lock-operator">]</span>
<span class="org-tuareg-font-lock-governing">end</span><span class="org-tuareg-font-lock-operator">;</span>
</pre>
</div>
<p>
Then, define what to do with the arguments:
</p>
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">let</span> <span class="org-variable-name">c</span> <span class="org-tuareg-font-lock-operator">=</span>
<span class="org-tuareg-font-lock-module">Command_line.</span>get_bool <span class="org-string">"check"</span>
<span class="org-tuareg-font-lock-governing">in</span>
<span class="org-tuareg-font-lock-governing">let</span> <span class="org-variable-name">basis</span> <span class="org-tuareg-font-lock-operator">=</span>
<span class="org-keyword">match</span> <span class="org-tuareg-font-lock-module">Command_line.</span>get <span class="org-string">"basis"</span> <span class="org-keyword">with</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Some</span> x <span class="org-tuareg-font-lock-operator">-&gt;</span> x
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">None</span> <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-keyword">assert</span> <span class="org-constant">false</span>
<span class="org-tuareg-font-lock-governing">in</span>
<span class="org-tuareg-font-lock-governing">let</span> <span class="org-variable-name">multiplicity</span> <span class="org-tuareg-font-lock-operator">=</span>
<span class="org-keyword">match</span> <span class="org-tuareg-font-lock-module">Command_line.</span>get <span class="org-string">"multiplicity"</span> <span class="org-keyword">with</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">None</span> <span class="org-tuareg-font-lock-operator">-&gt;</span> 1
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Some</span> n <span class="org-tuareg-font-lock-operator">-&gt;</span> int_of_string n
<span class="org-tuareg-font-lock-governing">in</span>
</pre>
</div>
</div>
<div id="outline-container-orgf56b3ee" class="outline-3">
<h3 id="orgf56b3ee"><span class="section-number-3">4.1</span> Type</h3>
<div class="outline-text-3" id="text-4-1">
<div class="org-src-container">
<pre class="src src-ocaml" id="org760c952"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">short_opt</span> <span class="org-tuareg-font-lock-operator">=</span> char
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">long_opt</span> <span class="org-tuareg-font-lock-operator">=</span> string
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">optional</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-tuareg-font-lock-constructor">Mandatory</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Optional</span>
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">documentation</span> <span class="org-tuareg-font-lock-operator">=</span> string
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">argument</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-tuareg-font-lock-constructor">With_arg</span> <span class="org-keyword">of</span> string <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Without_arg</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">With_opt_arg</span> <span class="org-keyword">of</span> string
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">description</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-tuareg-font-lock-operator">{</span>
short<span class="org-tuareg-font-lock-operator">:</span> short_opt <span class="org-tuareg-font-lock-operator">;</span>
long <span class="org-tuareg-font-lock-operator">:</span> long_opt <span class="org-tuareg-font-lock-operator">;</span>
opt <span class="org-tuareg-font-lock-operator">:</span> optional <span class="org-tuareg-font-lock-operator">;</span>
doc <span class="org-tuareg-font-lock-operator">:</span> documentation <span class="org-tuareg-font-lock-operator">;</span>
arg <span class="org-tuareg-font-lock-operator">:</span> argument <span class="org-tuareg-font-lock-operator">;</span>
<span class="org-tuareg-font-lock-operator">}</span>
</pre>
</div>
<ul class="org-ul">
<li>Short option: in the command line, a dash with a single character
(ex: <code>ls -l</code>)</li>
<li>Long option: in the command line, two dashes with a word
(ex: <code>ls --directory</code>)</li>
<li>Command-line options can be <code>Mandatory</code> or <code>Optional</code></li>
<li>Documentation of the option is used in the help function</li>
<li>Some options require an argument (<code>ls --ignore="*.ml"</code> ), some
don't (<code>ls -l</code>) and for some arguments the argument is optional
(<code>git --log[=&lt;n&gt;]</code>)</li>
</ul>
</div>
</div>
<div id="outline-container-orgd87f5ce" class="outline-3">
<h3 id="orgd87f5ce"><span class="section-number-3">4.2</span> Mutable attributes</h3>
<div class="outline-text-3" id="text-4-2">
<p>
All the options are stored in the hash table <code>dict</code> where the key
is the long option and the value is a value of type <code>description</code>.
</p>
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">set_header_doc</span> <span class="org-tuareg-font-lock-operator">:</span> string <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">set_description_doc</span> <span class="org-tuareg-font-lock-operator">:</span> string <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">set_footer_doc</span> <span class="org-tuareg-font-lock-operator">:</span> string <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
<p>
Functions to set the header, footer and main description of the
documentation provided by the <code>help</code> function:
</p>
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">anonymous</span> <span class="org-tuareg-font-lock-operator">:</span> long_opt <span class="org-tuareg-font-lock-operator">-&gt;</span> optional <span class="org-tuareg-font-lock-operator">-&gt;</span> documentation <span class="org-tuareg-font-lock-operator">-&gt;</span> description
</pre>
</div>
<p>
Function to create an anonymous argument.
</p>
</div>
</div>
<div id="outline-container-org2aa0f74" class="outline-3">
<h3 id="org2aa0f74"><span class="section-number-3">4.3</span> Query functions</h3>
<div class="outline-text-3" id="text-4-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">get</span> <span class="org-tuareg-font-lock-operator">:</span> long_opt <span class="org-tuareg-font-lock-operator">-&gt;</span> string option
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">get_bool</span> <span class="org-tuareg-font-lock-operator">:</span> long_opt <span class="org-tuareg-font-lock-operator">-&gt;</span> bool
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">anon_args</span> <span class="org-tuareg-font-lock-operator">:</span> unit <span class="org-tuareg-font-lock-operator">-&gt;</span> string list
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>get</code></td>
<td class="org-left">Returns the argument associated with a long option</td>
</tr>
<tr>
<td class="org-left"><code>get_bool</code></td>
<td class="org-left">True if the <code>Optional</code> argument is present in the command-line</td>
</tr>
<tr>
<td class="org-left"><code>anon_args</code></td>
<td class="org-left">Returns the list of anonymous arguments</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org6289fa0" class="outline-3">
<h3 id="org6289fa0"><span class="section-number-3">4.4</span> Specification</h3>
<div class="outline-text-3" id="text-4-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">set_specs</span> <span class="org-tuareg-font-lock-operator">:</span> description list <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
<p>
Sets the specifications of the current program from a list of
<code>descrption</code> variables.
</p>
</div>
</div>
</div>
<div id="outline-container-orgf025e44" class="outline-2">
<h2 id="orgf025e44"><span class="section-number-2">5</span> Constants</h2>
<div class="outline-text-2" id="text-5">
<p>
All constants used in the program.
</p>
</div>
<div id="outline-container-org54df39c" class="outline-3">
<h3 id="org54df39c"><span class="section-number-3">5.1</span> Thresholds</h3>
<div class="outline-text-3" id="text-5-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">epsilon</span> <span class="org-tuareg-font-lock-operator">:</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">integrals_cutoff</span> <span class="org-tuareg-font-lock-operator">:</span> float
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>epsilon</code></td>
<td class="org-left">Value below which a float is considered null. Default is &epsilon; = 2.10<sup>-15</sup></td>
</tr>
<tr>
<td class="org-left"><code>integrals_cutoff</code></td>
<td class="org-left">Cutoff value for integrals. Default is &epsilon;</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org7754673" class="outline-3">
<h3 id="org7754673"><span class="section-number-3">5.2</span> Mathematical constants</h3>
<div class="outline-text-3" id="text-5-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pi</span> <span class="org-tuareg-font-lock-operator">:</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">two_pi</span> <span class="org-tuareg-font-lock-operator">:</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">sq_pi</span> <span class="org-tuareg-font-lock-operator">:</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">sq_pi_over_two</span> <span class="org-tuareg-font-lock-operator">:</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pi_inv</span> <span class="org-tuareg-font-lock-operator">:</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">two_over_sq_pi</span> <span class="org-tuareg-font-lock-operator">:</span> float
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>pi</code></td>
<td class="org-left">\(\pi = 3.141~592~653~589~793~12\)</td>
</tr>
<tr>
<td class="org-left"><code>two_pi</code></td>
<td class="org-left">\(2 \pi\)</td>
</tr>
<tr>
<td class="org-left"><code>sq_pi</code></td>
<td class="org-left">\(\sqrt{\pi}\)</td>
</tr>
<tr>
<td class="org-left"><code>sq_pi_over_two</code></td>
<td class="org-left">\(\sqrt{\pi} / 2\)</td>
</tr>
<tr>
<td class="org-left"><code>pi_inv</code></td>
<td class="org-left">\(1 / \pi\)</td>
</tr>
<tr>
<td class="org-left"><code>two_over_sq_pi</code></td>
<td class="org-left">\(2 / \sqrt{\pi}\)</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org4a6d922" class="outline-3">
<h3 id="org4a6d922"><span class="section-number-3">5.3</span> Physical constants</h3>
<div class="outline-text-3" id="text-5-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">a0</span> <span class="org-tuareg-font-lock-operator">:</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">a0_inv</span> <span class="org-tuareg-font-lock-operator">:</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">ha_to_ev</span> <span class="org-tuareg-font-lock-operator">:</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">ev_to_ha</span> <span class="org-tuareg-font-lock-operator">:</span> float
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>a0</code></td>
<td class="org-left">Bohr's radius : \(a_0 = 0.529~177~210~67(23)\) angstrom</td>
</tr>
<tr>
<td class="org-left"><code>a0_inv</code></td>
<td class="org-left">\(1 / a_0\)</td>
</tr>
<tr>
<td class="org-left"><code>ha_to_ev</code></td>
<td class="org-left">Hartree to eV conversion factor : \(27.211~386~02(17)\)</td>
</tr>
<tr>
<td class="org-left"><code>ev_to_ha</code></td>
<td class="org-left">eV to Hartree conversion factor : 1 / <code>ha_to_ev</code></td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div id="outline-container-org12d227a" class="outline-2">
<h2 id="org12d227a"><span class="section-number-2">6</span> Coordinate</h2>
<div class="outline-text-2" id="text-6">
<p>
Coordinates in 3D space.
</p>
<p>
All operations on points are done in atomic units. Therefore,
all coordinates are given in bohr and manipulated with this
module.
</p>
</div>
<div id="outline-container-org62fcc02" class="outline-3">
<h3 id="org62fcc02"><span class="section-number-3">6.1</span> Type</h3>
<div class="outline-text-3" id="text-6-1">
<div class="org-src-container">
<pre class="src src-ocaml" id="orga70a4f3"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">bohr</span>
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">angstrom</span>
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">xyz</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-tuareg-font-lock-operator">{</span>
x <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">;</span>
y <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">;</span>
z <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">;</span>
<span class="org-tuareg-font-lock-operator">}</span>
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">'a point</span> <span class="org-tuareg-font-lock-operator">=</span> xyz
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span> <span class="org-tuareg-font-lock-operator">=</span> bohr point
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">axis</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-tuareg-font-lock-constructor">X</span> <span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Y</span> <span class="org-tuareg-font-lock-operator">|</span> Z
</pre>
</div>
</div>
</div>
<div id="outline-container-orga380f75" class="outline-3">
<h3 id="orga380f75"><span class="section-number-3">6.2</span> Creation</h3>
<div class="outline-text-3" id="text-6-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">make</span> <span class="org-tuareg-font-lock-operator">:</span> 'a point <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">make_angstrom</span> <span class="org-tuareg-font-lock-operator">:</span> 'a point <span class="org-tuareg-font-lock-operator">-&gt;</span> angstrom point
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">zero</span> <span class="org-tuareg-font-lock-operator">:</span> bohr point
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>make</code></td>
<td class="org-left">Creates a point in atomic units</td>
</tr>
<tr>
<td class="org-left"><code>make_angstrom</code></td>
<td class="org-left">Creates a point in angstrom</td>
</tr>
<tr>
<td class="org-left"><code>zero</code></td>
<td class="org-left">\((0., 0., 0.)\)</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org7f6d675" class="outline-3">
<h3 id="org7f6d675"><span class="section-number-3">6.3</span> Conversion</h3>
<div class="outline-text-3" id="text-6-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">bohr_to_angstrom</span> <span class="org-tuareg-font-lock-operator">:</span> bohr point <span class="org-tuareg-font-lock-operator">-&gt;</span> angstrom point
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">angstrom_to_bohr</span> <span class="org-tuareg-font-lock-operator">:</span> angstrom point <span class="org-tuareg-font-lock-operator">-&gt;</span> bohr point
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>bohr_to_angstrom</code></td>
<td class="org-left">Converts a point in bohr to angstrom</td>
</tr>
<tr>
<td class="org-left"><code>angstrom_to_bohr</code></td>
<td class="org-left">Converts a point in angstrom to bohr</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org925ab51" class="outline-3">
<h3 id="org925ab51"><span class="section-number-3">6.4</span> Vector operations</h3>
<div class="outline-text-3" id="text-6-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">neg</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">get</span> <span class="org-tuareg-font-lock-operator">:</span> axis <span class="org-tuareg-font-lock-operator">-&gt;</span> bohr point <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">dot</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">norm</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-tuareg-font-lock-operator">(</span> <span class="org-tuareg-font-lock-operator">|</span>. <span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-tuareg-font-lock-operator">(</span> <span class="org-tuareg-font-lock-operator">|+</span> <span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-tuareg-font-lock-operator">(</span> <span class="org-tuareg-font-lock-operator">|-</span> <span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>neg</code></td>
<td class="org-left">Negative of a point</td>
</tr>
<tr>
<td class="org-left"><code>get</code></td>
<td class="org-left">Extracts the projection of the coordinate on an axis</td>
</tr>
<tr>
<td class="org-left"><code>dot</code></td>
<td class="org-left">Dot product</td>
</tr>
<tr>
<td class="org-left"><code>norm</code></td>
<td class="org-left">\(\ell{^2}\) norm of the vector</td>
</tr>
<tr>
<td class="org-left"><code>¦.</code></td>
<td class="org-left">Scales the vector by a constant</td>
</tr>
<tr>
<td class="org-left"><code>¦+</code></td>
<td class="org-left">Adds two vectors</td>
</tr>
<tr>
<td class="org-left"><code>¦-</code></td>
<td class="org-left">Subtracts two vectors</td>
</tr>
</tbody>
</table>
<pre class="example" id="orgbe2f14a">
Coordinate.neg { x=1. ; y=2. ; z=3. } ;;
- : Coordinate.t = -1.0000 -2.0000 -3.0000
Coordinate.(get Y { x=1. ; y=2. ; z=3. }) ;;
- : float = 2.
Coordinate.(
2. |. { x=1. ; y=2. ; z=3. }
) ;;
- : Coordinate.t = 2.0000 4.0000 6.0000
Coordinate.(
{ x=1. ; y=2. ; z=3. } |+ { x=2. ; y=3. ; z=1. }
);;
- : Coordinate.t = 3.0000 5.0000 4.0000
Coordinate.(
{ x=1. ; y=2. ; z=3. } |- { x=2. ; y=3. ; z=1. }
);;
- : Coordinate.t = -1.0000 -1.0000 2.0000
</pre>
</div>
</div>
<div id="outline-container-orgc043b39" class="outline-3">
<h3 id="orgc043b39"><span class="section-number-3">6.5</span> Printers</h3>
<div class="outline-text-3" id="text-6-5">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp_bohr</span><span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp_angstrom</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
<p>
Coordinates can be printed in bohr or angstrom.
</p>
</div>
</div>
</div>
<div id="outline-container-org1923bd8" class="outline-2">
<h2 id="org1923bd8"><span class="section-number-2">7</span> Non-negative float</h2>
<div class="outline-text-2" id="text-7">
</div>
<div id="outline-container-orgbcd34bb" class="outline-3">
<h3 id="orgbcd34bb"><span class="section-number-3">7.1</span> Type</h3>
<div class="outline-text-3" id="text-7-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-keyword">private</span> float
</pre>
</div>
</div>
</div>
<div id="outline-container-orgbe46fd2" class="outline-3">
<h3 id="orgbe46fd2"><span class="section-number-3">7.2</span> Conversions</h3>
<div class="outline-text-3" id="text-7-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_float</span> <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">unsafe_of_float</span> <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_float</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_string</span> <span class="org-tuareg-font-lock-operator">:</span> string <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_string</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> string
</pre>
</div>
<p>
The <code>of_float</code> function checks that the float is non-negative.
The unsafe variant doesn't do this check.
</p>
</div>
</div>
</div>
<div id="outline-container-org8d1e251" class="outline-2">
<h2 id="org8d1e251"><span class="section-number-2">8</span> Powers</h2>
<div class="outline-text-2" id="text-8">
<p>
Contains powers of x, y and z describing the polynomials in atomic basis sets.
</p>
</div>
<div id="outline-container-org2427f71" class="outline-3">
<h3 id="org2427f71"><span class="section-number-3">8.1</span> Type</h3>
<div class="outline-text-3" id="text-8-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-keyword">private</span> <span class="org-tuareg-font-lock-operator">{</span>
x <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">;</span>
y <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">;</span>
z <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">;</span>
tot <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">;</span>
<span class="org-tuareg-font-lock-operator">}</span>
</pre>
</div>
<p>
<code>tot</code> always contains <code>x+y+z</code>.
</p>
</div>
</div>
<div id="outline-container-orgcb55052" class="outline-3">
<h3 id="orgcb55052"><span class="section-number-3">8.2</span> Conversions</h3>
<div class="outline-text-3" id="text-8-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_int_tuple</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">*</span> int <span class="org-tuareg-font-lock-operator">*</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_int_tuple</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">*</span> int <span class="org-tuareg-font-lock-operator">*</span> int
</pre>
</div>
<pre class="example" id="org9b264cf">
Powers.of_int_tuple (2,3,1);;
- : Powers.t = x^2 + y^3 + z^1
Powers.(to_int_tuple (of_int_tuple (2,3,1)));;
- : int * int * int = (2, 3, 1)
</pre>
</div>
</div>
<div id="outline-container-org744d5ef" class="outline-3">
<h3 id="org744d5ef"><span class="section-number-3">8.3</span> Operations</h3>
<div class="outline-text-3" id="text-8-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">get</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Coordinate.</span>axis <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">incr</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Coordinate.</span>axis <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">decr</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Coordinate.</span>axis <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>get</code></td>
<td class="org-left">Returns the value of the power for \(x\), \(y\) or \(z\)</td>
</tr>
<tr>
<td class="org-left"><code>incr</code></td>
<td class="org-left">Returns a new <code>Powers.t</code> with the power on the given axis incremented</td>
</tr>
<tr>
<td class="org-left"><code>decr</code></td>
<td class="org-left">Returns a new <code>Powers.t</code> with the power on the given axis decremented. As opposed to <code>of_int_tuple</code>, the values may become negative</td>
</tr>
</tbody>
</table>
<pre class="example" id="orgd4044dd">
Powers.get Coordinate.Y (Powers.of_int_tuple (2,3,1));;
- : int = 3
Powers.incr Coordinate.Y (Powers.of_int_tuple (2,3,1));;
- : Powers.t = x^2 + y^4 + z^1
Powers.decr Coordinate.Y (Powers.of_int_tuple (2,3,1));;
- : Powers.t = x^2 + y^2 + z^1
</pre>
</div>
</div>
<div id="outline-container-orgd52d720" class="outline-3">
<h3 id="orgd52d720"><span class="section-number-3">8.4</span> Printers</h3>
<div class="outline-text-3" id="text-8-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org012eacd" class="outline-2">
<h2 id="org012eacd"><span class="section-number-2">9</span> QCaml</h2>
<div class="outline-text-2" id="text-9">
<p>
QCaml-specific parameters
</p>
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">root</span> <span class="org-tuareg-font-lock-operator">:</span> string
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">name</span> <span class="org-tuareg-font-lock-operator">:</span> string
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>root</code></td>
<td class="org-left">Path to the QCaml source directory</td>
</tr>
<tr>
<td class="org-left"><code>name</code></td>
<td class="org-left"><code>"QCaml"</code></td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgba955b4" class="outline-2">
<h2 id="orgba955b4"><span class="section-number-2">10</span> Range</h2>
<div class="outline-text-2" id="text-10">
<p>
A range is a sorted list of integers in an interval.
</p>
<ul class="org-ul">
<li><code>"[a-b]"</code> : range between a and b (included)</li>
<li><code>"[a]"</code> : the list with only one integer a</li>
<li><code>"a"</code> : equivalent to "[a]"</li>
<li><code>"[36-53,72-107,126-131]"</code> represents the list of integers
[ 37 ; 37 ; 38 ; &#x2026; ; 52 ; 53 ; 72 ; 73 ; &#x2026; ; 106 ; 107 ; 126 ; 127 ; &#x2026; ; 130 ; 131 ].</li>
</ul>
</div>
<div id="outline-container-orgc921ed3" class="outline-3">
<h3 id="orgc921ed3"><span class="section-number-3">10.1</span> Type</h3>
<div class="outline-text-3" id="text-10-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orga7b85a3" class="outline-3">
<h3 id="orga7b85a3"><span class="section-number-3">10.2</span> Conversion</h3>
<div class="outline-text-3" id="text-10-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_string</span> <span class="org-tuareg-font-lock-operator">:</span> string <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_string</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> string
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_int_list</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int list
</pre>
</div>
</div>
</div>
<div id="outline-container-org92dc675" class="outline-3">
<h3 id="org92dc675"><span class="section-number-3">10.3</span> Printers</h3>
<div class="outline-text-3" id="text-10-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-orgc8e5623" class="outline-2">
<h2 id="orgc8e5623"><span class="section-number-2">11</span> Spin</h2>
<div class="outline-text-2" id="text-11">
<p>
Electron spin
</p>
</div>
<div id="outline-container-orge61ea06" class="outline-3">
<h3 id="orge61ea06"><span class="section-number-3">11.1</span> Type</h3>
<div class="outline-text-3" id="text-11-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-tuareg-font-lock-constructor">Alfa</span> <span class="org-tuareg-font-lock-operator">|</span> Beta
</pre>
</div>
<p>
Note :
<code>Alfa</code> if written with an 'f' instead of 'ph' because it has the same number of
letters as <code>Beta</code>, so the alignment of the code is nicer.
</p>
</div>
</div>
<div id="outline-container-orgb870fcb" class="outline-3">
<h3 id="orgb870fcb"><span class="section-number-3">11.2</span> Functions</h3>
<div class="outline-text-3" id="text-11-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">other</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
</pre>
</div>
<p>
Returns the opposite spin
</p>
</div>
</div>
<div id="outline-container-orgd0f4806" class="outline-3">
<h3 id="orgd0f4806"><span class="section-number-3">11.3</span> Printers</h3>
<div class="outline-text-3" id="text-11-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org30d2221" class="outline-2">
<h2 id="org30d2221"><span class="section-number-2">12</span> Util</h2>
<div class="outline-text-2" id="text-12">
<p>
Utility functions.
</p>
</div>
<div id="outline-container-orgba158b9" class="outline-3">
<h3 id="orgba158b9"><span class="section-number-3">12.1</span> External C functions</h3>
<div class="outline-text-3" id="text-12-1">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>erf_float</code></td>
<td class="org-left">Error function <code>erf</code> from <code>libm</code></td>
</tr>
<tr>
<td class="org-left"><code>erfc_float</code></td>
<td class="org-left">Complementary error function <code>erfc</code> from <code>libm</code></td>
</tr>
<tr>
<td class="org-left"><code>gamma_float</code></td>
<td class="org-left">Gamma function <code>gamma</code> from <code>libm</code></td>
</tr>
<tr>
<td class="org-left"><code>popcnt</code></td>
<td class="org-left"><code>popcnt</code> instruction</td>
</tr>
<tr>
<td class="org-left"><code>trailz</code></td>
<td class="org-left"><code>ctz</code> instruction</td>
</tr>
<tr>
<td class="org-left"><code>leadz</code></td>
<td class="org-left"><code>bsf</code> instruction</td>
</tr>
</tbody>
</table>
</div>
<div id="outline-container-org5a22bbb" class="outline-4">
<h4 id="org5a22bbb"><span class="section-number-4">12.1.1</span> Erf</h4>
<div class="outline-text-4" id="text-12-1-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">external</span> <span class="org-function-name">erf_float</span> <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> float <span class="org-tuareg-font-lock-operator">=</span> <span class="org-string">"erf_float_bytecode"</span> <span class="org-string">"erf_float"</span> <span class="org-tuareg-font-lock-attribute">[@@unboxed]</span> <span class="org-tuareg-font-lock-attribute">[@@noalloc]</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org3e8d069" class="outline-4">
<h4 id="org3e8d069"><span class="section-number-4">12.1.2</span> Erfc</h4>
<div class="outline-text-4" id="text-12-1-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">external</span> <span class="org-function-name">erfc_float</span> <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> float <span class="org-tuareg-font-lock-operator">=</span> <span class="org-string">"erfc_float_bytecode"</span> <span class="org-string">"erfc_float"</span> <span class="org-tuareg-font-lock-attribute">[@@unboxed]</span> <span class="org-tuareg-font-lock-attribute">[@@noalloc]</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgb4df3c2" class="outline-4">
<h4 id="orgb4df3c2"><span class="section-number-4">12.1.3</span> Gamma</h4>
<div class="outline-text-4" id="text-12-1-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">external</span> <span class="org-function-name">gamma_float</span> <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> float <span class="org-tuareg-font-lock-operator">=</span> <span class="org-string">"gamma_float_bytecode"</span> <span class="org-string">"gamma_float"</span> <span class="org-tuareg-font-lock-attribute">[@@unboxed]</span> <span class="org-tuareg-font-lock-attribute">[@@noalloc]</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org6c5d330" class="outline-4">
<h4 id="org6c5d330"><span class="section-number-4">12.1.4</span> Popcnt</h4>
<div class="outline-text-4" id="text-12-1-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">popcnt</span> <span class="org-tuareg-font-lock-operator">:</span> int64 <span class="org-tuareg-font-lock-operator">-&gt;</span> int
</pre>
</div>
</div>
</div>
<div id="outline-container-orgdfb5f51" class="outline-4">
<h4 id="orgdfb5f51"><span class="section-number-4">12.1.5</span> Trailz</h4>
<div class="outline-text-4" id="text-12-1-5">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">trailz</span> <span class="org-tuareg-font-lock-operator">:</span> int64 <span class="org-tuareg-font-lock-operator">-&gt;</span> int
</pre>
</div>
</div>
</div>
<div id="outline-container-org3eb911e" class="outline-4">
<h4 id="org3eb911e"><span class="section-number-4">12.1.6</span> Leadz</h4>
<div class="outline-text-4" id="text-12-1-6">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">leadz</span> <span class="org-tuareg-font-lock-operator">:</span> int64 <span class="org-tuareg-font-lock-operator">-&gt;</span> int
</pre>
</div>
</div>
</div>
<div id="outline-container-org2d822a2" class="outline-4">
<h4 id="org2d822a2"><span class="section-number-4">12.1.7</span> Test</h4>
</div>
</div>
<div id="outline-container-org8e236a2" class="outline-3">
<h3 id="org8e236a2"><span class="section-number-3">12.2</span> General functions</h3>
<div class="outline-text-3" id="text-12-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">fact</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-comment-delimiter">(* </span><span class="org-comment">@raise Invalid_argument for negative arguments or arguments &gt;100. </span><span class="org-comment-delimiter">*)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">binom</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">binom_float</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">chop</span> <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-operator">(</span>unit <span class="org-tuareg-font-lock-operator">-&gt;</span> float<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pow</span> <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">float_of_int_fast</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_some</span> <span class="org-tuareg-font-lock-operator">:</span> 'a option <span class="org-tuareg-font-lock-operator">-&gt;</span> 'a
<span class="org-keyword">exception</span> <span class="org-tuareg-font-lock-constructor">Not_implemented</span> <span class="org-keyword">of</span> string
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">not_implemented</span> <span class="org-tuareg-font-lock-operator">:</span> string <span class="org-tuareg-font-lock-operator">-&gt;</span> 'a
<span class="org-comment-delimiter">(* </span><span class="org-comment">@raise Not_implemented. </span><span class="org-comment-delimiter">*)</span>
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>fact</code></td>
<td class="org-left">Factorial function.</td>
</tr>
<tr>
<td class="org-left"><code>binom</code></td>
<td class="org-left">Binomial coefficient. <code>binom n k</code> = \(C_n^k\)</td>
</tr>
<tr>
<td class="org-left"><code>binom_float</code></td>
<td class="org-left">float variant of <code>binom</code></td>
</tr>
<tr>
<td class="org-left"><code>pow</code></td>
<td class="org-left">Fast implementation of the power function for small integer powers</td>
</tr>
<tr>
<td class="org-left"><code>chop</code></td>
<td class="org-left">In <code>chop a f</code>, evaluate <code>f</code> only if the absolute value of <code>a</code> is larger than <code>Constants.epsilon</code>, and return <code>a *. f ()</code>.</td>
</tr>
<tr>
<td class="org-left"><code>float_of_int_fast</code></td>
<td class="org-left">Faster implementation of float<sub>of</sub><sub>int</sub> for small positive ints</td>
</tr>
<tr>
<td class="org-left"><code>not_implemented</code></td>
<td class="org-left">Fails if some functionality is not implemented</td>
</tr>
<tr>
<td class="org-left"><code>of_some</code></td>
<td class="org-left">Extracts the value of an option</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org129b6ff" class="outline-3">
<h3 id="org129b6ff"><span class="section-number-3">12.3</span> Functions related to the Boys function</h3>
<div class="outline-text-3" id="text-12-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">incomplete_gamma</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-label">alpha</span><span class="org-tuareg-font-lock-operator">:</span>float <span class="org-tuareg-font-lock-operator">-&gt;</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-comment-delimiter">(* </span><span class="org-comment">@raise Failure when the calculation doesn't converge. </span><span class="org-comment-delimiter">*)</span>
</pre>
</div>
<p>
The lower <a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">Incomplete Gamma function</a> is implemented :
\[
\gamma(\alpha,x) = \int_0^x e^{-t} t^{\alpha-1} dt
\]
</p>
<p>
p: \(\frac{1}{\Gamma(\alpha)} \int_0^x e^{-t} t^{\alpha-1} dt\)
</p>
<p>
q: \(\frac{1}{\Gamma(\alpha)} \int_x^\infty e^{-t} t^{\alpha-1} dt\)
</p>
<p>
Reference : Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
(New Algorithm handbook in C language) (Gijyutsu hyouron sha,
Tokyo, 1991) p.227 [in Japanese]
</p>
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">boys_function</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-label">maxm</span><span class="org-tuareg-font-lock-operator">:</span>int <span class="org-tuareg-font-lock-operator">-&gt;</span> float <span class="org-tuareg-font-lock-operator">-&gt;</span> float array
</pre>
</div>
<p>
The <a href="https://link.springer.com/article/10.1007/s10910-005-9023-3">Generalized Boys function</a> is implemented,
<code>maxm</code> is the maximum total angular momentum.
</p>
<p>
\[
F_m(x) = \frac{\gamma(m+1/2,x)}{2x^{m+1/2}}
\]
where \(\gamma\) is the incomplete gamma function.
</p>
<ul class="org-ul">
<li>\(F_0(0.) = 1\)</li>
<li>\(F_0(t) = \frac{\sqrt{\pi}}{2\sqrt{t}} \text{erf} ( \sqrt{t} )\)</li>
<li>\(F_m(0.) = \frac{1}{2m+1}\)</li>
<li>\(F_m(t) = \frac{\gamma{m+1/2,t}}{2t^{m+1/2}}\)</li>
<li>\(F_m(t) = \frac{ 2t\, F_{m+1}(t) + e^{-t} }{2m+1}\)</li>
</ul>
</div>
</div>
<div id="outline-container-org0b6cdc7" class="outline-3">
<h3 id="org0b6cdc7"><span class="section-number-3">12.4</span> List functions</h3>
<div class="outline-text-3" id="text-12-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">list_some</span> <span class="org-tuareg-font-lock-operator">:</span> 'a option list <span class="org-tuareg-font-lock-operator">-&gt;</span> 'a list
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">list_range</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int list
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">list_pack</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> 'a list <span class="org-tuareg-font-lock-operator">-&gt;</span> 'a list list
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>list_some</code></td>
<td class="org-left">Filters out all <code>None</code> elements of the list, and returns the elements without the <code>Some</code></td>
</tr>
<tr>
<td class="org-left"><code>list_range</code></td>
<td class="org-left">Creates a list of consecutive integers</td>
</tr>
<tr>
<td class="org-left"><code>list_pack</code></td>
<td class="org-left"><code>list_pack n l</code> Creates a list of <code>n</code>-elements lists</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org91499d0" class="outline-3">
<h3 id="org91499d0"><span class="section-number-3">12.5</span> Array functions</h3>
<div class="outline-text-3" id="text-12-5">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">array_range</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int array
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">array_sum</span> <span class="org-tuareg-font-lock-operator">:</span> float array <span class="org-tuareg-font-lock-operator">-&gt;</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">array_product</span> <span class="org-tuareg-font-lock-operator">:</span> float array <span class="org-tuareg-font-lock-operator">-&gt;</span> float
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>array_range</code></td>
<td class="org-left">Creates an array of consecutive integers</td>
</tr>
<tr>
<td class="org-left"><code>array_sum</code></td>
<td class="org-left">Returns the sum of all the elements of the array</td>
</tr>
<tr>
<td class="org-left"><code>array_product</code></td>
<td class="org-left">Returns the product of all the elements of the array</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org96db98c" class="outline-3">
<h3 id="org96db98c"><span class="section-number-3">12.6</span> Stream functions</h3>
<div class="outline-text-3" id="text-12-6">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">stream_range</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-module">Stream.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">stream_to_list</span> <span class="org-tuareg-font-lock-operator">:</span> 'a <span class="org-tuareg-font-lock-module">Stream.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> 'a list
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">stream_fold</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-operator">(</span>'a <span class="org-tuareg-font-lock-operator">-&gt;</span> 'b <span class="org-tuareg-font-lock-operator">-&gt;</span> 'a<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">-&gt;</span> 'a <span class="org-tuareg-font-lock-operator">-&gt;</span> 'b <span class="org-tuareg-font-lock-module">Stream.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> 'a
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>stream_range</code></td>
<td class="org-left">Creates a stream returning consecutive integers</td>
</tr>
<tr>
<td class="org-left"><code>stream_to_list</code></td>
<td class="org-left">Read a stream and put items in a list</td>
</tr>
<tr>
<td class="org-left"><code>stream_fold</code></td>
<td class="org-left">Apply a fold to the elements of the stream</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgbf0f986" class="outline-3">
<h3 id="orgbf0f986"><span class="section-number-3">12.7</span> Printers</h3>
<div class="outline-text-3" id="text-12-7">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp_float_array_size</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> float array <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp_float_array</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> float array <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp_float_2darray_size</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> float array array <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp_float_2darray</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> float array array <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp_bitstring</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Z.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>pp_float_array</code></td>
<td class="org-left">Printer for float arrays</td>
</tr>
<tr>
<td class="org-left"><code>pp_float_array_size</code></td>
<td class="org-left">Printer for float arrays with size</td>
</tr>
<tr>
<td class="org-left"><code>pp_float_2darray</code></td>
<td class="org-left">Printer for matrices</td>
</tr>
<tr>
<td class="org-left"><code>pp_float_2darray_size</code></td>
<td class="org-left">Printer for matrices with size</td>
</tr>
<tr>
<td class="org-left"><code>pp_bitstring</code></td>
<td class="org-left">Printer for bit strings (used by <code>Bitstring</code> module)</td>
</tr>
</tbody>
</table>
<pre class="example" id="org1916228">
pp_float_array_size:
[ 6: 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ]
pp_float_array:
[ 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ]
pp_float_2darray_size
[
2:[ 6: 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ]
[ 4: 1.000000 2.000000 3.000000 4.000000 ] ]
pp_float_2darray:
[ [ 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ]
[ 1.000000 2.000000 3.000000 4.000000 ] ]
pp_bitstring 14:
+++++------+--
</pre>
</div>
</div>
</div>
<div id="outline-container-org912d5d1" class="outline-2">
<h2 id="org912d5d1"><span class="section-number-2">13</span> Zkey</h2>
<div class="outline-text-2" id="text-13">
<p>
Encodes the powers of x, y, z in a compact form, suitable for being
used as keys in a hash table.
</p>
<p>
Internally, the <code>Zkey.t</code> is made of two integers, <code>left</code> and <code>right</code>.
The small integers x, y and z are stored compactly in this 126-bits
space:
</p>
<pre class="example" id="org70e667d">
Left Right
3 [--------------------------------------------------------------] [------------------|---------------|---------------|---------------]
x y z
6 [--------------------------------------------------------------] [---|----------|----------|----------|----------|----------|---------]
x1 y1 z1 x2 y2 z2
9 [---------------------------------|----------|----------|---------] [---|----------|----------|----------|----------|----------|---------]
x1 y1 z1 x2 y2 z2 x3 y3 z3
12 [---|----------|----------|----------|----------|----------|---------] [---|----------|----------|----------|----------|----------|---------]
x1 y1 z1 x2 y2 z2 x3 y3 z3 x4 y4 z4
</pre>
<p>
The values of x,y,z should be positive and should not exceed 32767 for
<code>kind=3</code>. For all other kinds kinds the values should not exceed 1023.
</p>
</div>
<div id="outline-container-org001f90b" class="outline-3">
<h3 id="org001f90b"><span class="section-number-3">13.1</span> Types</h3>
<div class="outline-text-3" id="text-13-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span>
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">kind</span> <span class="org-tuareg-font-lock-operator">=</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Three</span> <span class="org-keyword">of</span> <span class="org-tuareg-font-lock-module">Powers.</span>t
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Four</span> <span class="org-keyword">of</span> <span class="org-tuareg-font-lock-operator">(</span>int <span class="org-tuareg-font-lock-operator">*</span> int <span class="org-tuareg-font-lock-operator">*</span> int <span class="org-tuareg-font-lock-operator">*</span> int<span class="org-tuareg-font-lock-operator">)</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Six</span> <span class="org-keyword">of</span> <span class="org-tuareg-font-lock-operator">(</span><span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">*</span> <span class="org-tuareg-font-lock-module">Powers.</span>t<span class="org-tuareg-font-lock-operator">)</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Nine</span> <span class="org-keyword">of</span> <span class="org-tuareg-font-lock-operator">(</span><span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">*</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">*</span> <span class="org-tuareg-font-lock-module">Powers.</span>t<span class="org-tuareg-font-lock-operator">)</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Twelve</span> <span class="org-keyword">of</span> <span class="org-tuareg-font-lock-operator">(</span><span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">*</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">*</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">*</span> <span class="org-tuareg-font-lock-module">Powers.</span>t<span class="org-tuareg-font-lock-operator">)</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org9ac062e" class="outline-3">
<h3 id="org9ac062e"><span class="section-number-3">13.2</span> Conversions</h3>
<div class="outline-text-3" id="text-13-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_powers_three</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_powers_six</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_powers_nine</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_powers_twelve</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_powers</span> <span class="org-tuareg-font-lock-operator">:</span> kind <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_int_array</span> <span class="org-tuareg-font-lock-operator">:</span> int array <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_int_four</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_int_array</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int array
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_powers</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> kind
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_string</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> string
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>of_powers_three</code></td>
<td class="org-left">Create from a <code>Powers.t</code></td>
</tr>
<tr>
<td class="org-left"><code>of_powers_six</code></td>
<td class="org-left">Create from two <code>Powers.t</code></td>
</tr>
<tr>
<td class="org-left"><code>of_powers_nine</code></td>
<td class="org-left">Create from three <code>Powers.t</code></td>
</tr>
<tr>
<td class="org-left"><code>of_powers_twelve</code></td>
<td class="org-left">Create from four <code>Powers.t</code></td>
</tr>
<tr>
<td class="org-left"><code>of_powers</code></td>
<td class="org-left">Create using the <code>kind</code> type</td>
</tr>
<tr>
<td class="org-left"><code>of_int_array</code></td>
<td class="org-left">Convert from an <code>int</code> array</td>
</tr>
<tr>
<td class="org-left"><code>of_int_four</code></td>
<td class="org-left">Create from four <code>ints</code></td>
</tr>
<tr>
<td class="org-left"><code>to_int_array</code></td>
<td class="org-left">Convert to an <code>int</code> array</td>
</tr>
<tr>
<td class="org-left"><code>to_powers</code></td>
<td class="org-left">Convert to an <code>Powers.t</code> array</td>
</tr>
<tr>
<td class="org-left"><code>to_string</code></td>
<td class="org-left">Pretty printing</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org6f8b1b7" class="outline-3">
<h3 id="org6f8b1b7"><span class="section-number-3">13.3</span> Functions for hash tables</h3>
<div class="outline-text-3" id="text-13-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">hash</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">equal</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> bool
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">compare</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>hash</code></td>
<td class="org-left">Associates a nonnegative integer to any Zkey</td>
</tr>
<tr>
<td class="org-left"><code>equal</code></td>
<td class="org-left">The equal function. True if two Zkeys are equal</td>
</tr>
<tr>
<td class="org-left"><code>compare</code></td>
<td class="org-left">Comparison function, used for sorting</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org0d32047" class="outline-3">
<h3 id="org0d32047"><span class="section-number-3">13.4</span> Printers</h3>
<div class="outline-text-3" id="text-13-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org39b0e68" class="outline-2">
<h2 id="org39b0e68"><span class="section-number-2">14</span> Zmap</h2>
<div class="outline-text-2" id="text-14">
<p>
A hash table where the keys are <code>Zkey</code>
</p>
</div>
<div id="outline-container-org43d8800" class="outline-3">
<h3 id="org43d8800"><span class="section-number-3">14.1</span> Type</h3>
<div class="outline-text-3" id="text-14-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">include</span> <span class="org-tuareg-font-lock-governing">module type of</span> <span class="org-tuareg-font-lock-module">Hashtbl.Make</span><span class="org-tuareg-font-lock-operator">(</span><span class="org-tuareg-font-lock-constructor">Zkey</span><span class="org-tuareg-font-lock-operator">)</span>
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Anthony Scemama</p>
<p class="date">Created: 2021-01-20 Wed 23:52</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
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