mirror of
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2441 lines
118 KiB
HTML
2441 lines
118 KiB
HTML
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/*]]>*/-->
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// @license magnet:?xt=urn:btih:e95b018ef3580986a04669f1b5879592219e2a7a&dn=public-domain.txt Public Domain
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</head>
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href=""> UP </a>
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<a accesskey="H" href="index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Common</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orga121b3f">1. Summary</a></li>
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<li><a href="#orge2e4658">2. Angular Momentum</a>
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<ul>
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<li><a href="#orgc3c79cb">2.1. Type</a></li>
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<li><a href="#org1074ea0">2.2. Conversions</a></li>
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<li><a href="#orgae17ac7">2.3. Shell functions</a></li>
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<li><a href="#orgf27e1b0">2.4. Arithmetic</a></li>
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<li><a href="#orgc1256af">2.5. Printers</a></li>
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<li><a href="#org5bccb0a">2.6. <span class="todo TODO">TODO</span> Tests</a></li>
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</ul>
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</li>
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<li><a href="#org3abdd03">3. Bit string</a>
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<ul>
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<li><a href="#org5c53764">3.1. Type</a></li>
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<li><a href="#org0952bd2">3.2. General implementation</a></li>
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<li><a href="#org9ed6ef7">3.3. Printers</a></li>
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</ul>
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</li>
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<li><a href="#org0e068a6">4. Charge</a>
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<ul>
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<li><a href="#org0f3ddfe">4.1. Type</a></li>
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<li><a href="#orga72d278">4.2. Conversions</a></li>
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<li><a href="#org9a51a22">4.3. Simple operations</a></li>
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<li><a href="#orgdc3ea1b">4.4. Printers</a></li>
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</ul>
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</li>
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<li><a href="#org8a2e506">5. Command line</a>
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<ul>
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<li><a href="#org73bf03e">5.1. Types</a></li>
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<li><a href="#org8fc90db">5.2. Mutable attributes</a></li>
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<li><a href="#org7bebbc6">5.3. Query functions</a></li>
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<li><a href="#orgd8571bd">5.4. Specification</a></li>
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</ul>
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</li>
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<li><a href="#orge207032">6. Constants</a>
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<ul>
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<li><a href="#org170850d">6.1. Thresholds</a></li>
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<li><a href="#org03d3547">6.2. Mathematical constants</a></li>
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<li><a href="#org7ed65ae">6.3. Physical constants</a></li>
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</ul>
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</li>
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<li><a href="#orga02825d">7. Coordinate</a>
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<ul>
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<li><a href="#org365ebd1">7.1. Type</a></li>
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<li><a href="#orgb1b5848">7.2. Creation</a></li>
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<li><a href="#orgcb1df76">7.3. Conversion</a></li>
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<li><a href="#org4ccf2ce">7.4. Vector operations</a></li>
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<li><a href="#org56e65fa">7.5. Printers</a></li>
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</ul>
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</li>
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<li><a href="#orgc46a22e">8. Non-negative float</a>
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<ul>
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<li><a href="#orgaf4f696">8.1. Type</a></li>
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<li><a href="#org46f8226">8.2. Conversions</a></li>
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</ul>
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</li>
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<li><a href="#orge23858f">9. Powers</a>
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<ul>
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<li><a href="#orgcce21a6">9.1. Type</a></li>
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<li><a href="#orgd2a54fc">9.2. Conversions</a></li>
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<li><a href="#org3d41f69">9.3. Operations</a></li>
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<li><a href="#orge1904b7">9.4. Printers</a></li>
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</ul>
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</li>
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<li><a href="#org67d3688">10. QCaml</a></li>
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<li><a href="#org604cc85">11. Range</a>
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<ul>
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<li><a href="#org02778b3">11.1. Type</a></li>
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<li><a href="#orgaa5c109">11.2. Conversion</a></li>
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<li><a href="#org936ca1b">11.3. Printers</a></li>
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</ul>
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</li>
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<li><a href="#org629a719">12. Spin</a>
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<ul>
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<li><a href="#org15a9bad">12.1. Type</a></li>
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<li><a href="#orgc66a44d">12.2. Functions</a></li>
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<li><a href="#org5ca9b50">12.3. Printers</a></li>
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</ul>
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</li>
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<li><a href="#org9d9c2bc">13. Util</a>
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<ul>
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<li><a href="#org47b536c">13.1. External C functions</a>
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<ul>
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<li><a href="#org733601a">13.1.1. Erf</a></li>
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<li><a href="#orgab0069e">13.1.2. Erfc</a></li>
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<li><a href="#orgd30e7a9">13.1.3. Gamma</a></li>
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<li><a href="#org1b63989">13.1.4. Popcnt</a></li>
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<li><a href="#orgdadaae7">13.1.5. Trailz</a></li>
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<li><a href="#org4fec5b6">13.1.6. Leadz</a></li>
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<li><a href="#org6af6934">13.1.7. Test</a></li>
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</ul>
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</li>
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<li><a href="#orgc1753fb">13.2. General functions</a></li>
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<li><a href="#org0e4e8b3">13.3. Functions related to the Boys function</a></li>
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<li><a href="#orga7ae962">13.4. List functions</a></li>
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<li><a href="#org5d2699c">13.5. Array functions</a></li>
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<li><a href="#orgbeccc98">13.6. Stream functions</a></li>
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<li><a href="#org2037fab">13.7. Printers</a></li>
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</ul>
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</li>
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<li><a href="#org06e4fd3">14. Zkey</a>
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<ul>
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<li><a href="#orgee81c34">14.1. Types</a></li>
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<li><a href="#orgf60d335">14.2. Conversions</a></li>
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<li><a href="#orgccdcb31">14.3. Functions for hash tables</a></li>
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<li><a href="#org4f18db8">14.4. Printers</a></li>
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</ul>
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</li>
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<li><a href="#org1a12374">15. Zmap</a>
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<ul>
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<li><a href="#org2ed0818">15.1. Type</a></li>
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</ul>
|
|
</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga121b3f" class="outline-2">
|
|
<h2 id="orga121b3f"><span class="section-number-2">1</span> Summary</h2>
|
|
</div>
|
|
|
|
<div id="outline-container-orge2e4658" class="outline-2">
|
|
<h2 id="orge2e4658"><span class="section-number-2">2</span> Angular Momentum</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<p>
|
|
Azimuthal quantum number, repsesented as \( s,p,d,\dots \) .
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc3c79cb" class="outline-3">
|
|
<h3 id="orgc3c79cb"><span class="section-number-3">2.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
<p>
|
|
<a id="org7175f3f"><code>Angular_momentum.t</code></a>
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml" id="org30079fe"><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 <a href="#org7175f3f"><code>Angular_momentum.t</code></a> 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-org1074ea0" class="outline-3">
|
|
<h3 id="org1074ea0"><span class="section-number-3">2.2</span> Conversions</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_char</span> <span class="org-tuareg-font-lock-operator">:</span> char <span class="org-tuareg-font-lock-operator">-></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">-></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">-></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">-></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">-></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 <a href="#org7175f3f"><code>Angular_momentum.t</code></a> 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>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org2fc0bc6">
|
|
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-orgae17ac7" class="outline-3">
|
|
<h3 id="orgae17ac7"><span class="section-number-3">2.3</span> Shell functions</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">n_functions</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-></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">-></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 <a href="#orga0e889d"><code>Zkey.t</code></a>, where each element is a a key associated with the the powers of \(x,y,z\).</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org72a12b4">
|
|
Angular_momentum.(n_functions D) ;;
|
|
- : int = 6
|
|
|
|
Angular_momentum.( zkey_array (Doublet (P,S)) );;
|
|
- : Zkey.t array =
|
|
[|< 01125899906842624 | 1, 0, 0, 0, 0, 0 >;
|
|
< 01099511627776 | 0, 1, 0, 0, 0, 0 >;
|
|
< 01073741824 | 0, 0, 1, 0, 0, 0 >|]
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf27e1b0" class="outline-3">
|
|
<h3 id="orgf27e1b0"><span class="section-number-3">2.4</span> Arithmetic</h3>
|
|
<div class="outline-text-3" id="text-2-4">
|
|
<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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></span> t
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="orgfcfc613">
|
|
Angular_momentum.(D + P);;
|
|
- : Angular_momentum.t = F
|
|
|
|
Angular_momentum.(F - P);;
|
|
- : Angular_momentum.t = D
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc1256af" class="outline-3">
|
|
<h3 id="orgc1256af"><span class="section-number-3">2.5</span> Printers</h3>
|
|
<div class="outline-text-3" id="text-2-5">
|
|
<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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></span> unit
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5bccb0a" class="outline-3">
|
|
<h3 id="org5bccb0a"><span class="section-number-3">2.6</span> <span class="todo TODO">TODO</span> Tests</h3>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org3abdd03" class="outline-2">
|
|
<h2 id="org3abdd03"><span class="section-number-2">3</span> Bit string</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<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-org5c53764" class="outline-3">
|
|
<h3 id="org5c53764"><span class="section-number-3">3.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
<p>
|
|
<a id="org6d05032"><code>Bitstring.t</code></a>
|
|
</p>
|
|
<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-org0952bd2" class="outline-3">
|
|
<h3 id="org0952bd2"><span class="section-number-3">3.2</span> General implementation</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_int</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-></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">-></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">-></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">-></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">-></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">-></span> int <span class="org-tuareg-font-lock-operator">-></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">-></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">-></span> int <span class="org-tuareg-font-lock-operator">-></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">-></span> int <span class="org-tuareg-font-lock-operator">-></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">-></span> int <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></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">-></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">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></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">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> int <span class="org-tuareg-font-lock-operator">-></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>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org71f9ac0">
|
|
Bitstring.of_int 15;;
|
|
- : Bitstring.t =
|
|
++++------------------------------------------------------------
|
|
</pre>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="orgfa71f45">
|
|
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>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org50c9185">
|
|
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>
|
|
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org46fa709">
|
|
Bitstring.(plus_one (of_int 15));;
|
|
- : Bitstring.t =
|
|
----+-----------------------------------------------------------
|
|
|
|
Bitstring.(minus_one (of_int 15));;
|
|
- : Bitstring.t =
|
|
-+++------------------------------------------------------------
|
|
</pre>
|
|
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org8112908">
|
|
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>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org8717a99">
|
|
Bitstring.(to_list (of_int 45));;
|
|
- : int list = [1; 3; 4; 6]
|
|
</pre>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="orgf15b6fe">
|
|
Bitstring.permutations 2 4;;
|
|
- : Bitstring.t list =
|
|
[++--------------------------------------------------------------;
|
|
+-+-------------------------------------------------------------;
|
|
-++-------------------------------------------------------------;
|
|
+--+------------------------------------------------------------;
|
|
-+-+------------------------------------------------------------;
|
|
--++------------------------------------------------------------]
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9ed6ef7" class="outline-3">
|
|
<h3 id="org9ed6ef7"><span class="section-number-3">3.3</span> Printers</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-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">-></span> t <span class="org-tuareg-font-lock-operator">-></span> unit
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0e068a6" class="outline-2">
|
|
<h2 id="org0e068a6"><span class="section-number-2">4</span> Charge</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
</div>
|
|
|
|
<div id="outline-container-org0f3ddfe" class="outline-3">
|
|
<h3 id="org0f3ddfe"><span class="section-number-3">4.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
<p>
|
|
<a id="org8761a74"><code>Charge.t</code></a>
|
|
</p>
|
|
<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,…).
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga72d278" class="outline-3">
|
|
<h3 id="orga72d278"><span class="section-number-3">4.2</span> Conversions</h3>
|
|
<div class="outline-text-3" id="text-4-2">
|
|
<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">-></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">-></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">-></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">-></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">-></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">-></span> string
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9a51a22" class="outline-3">
|
|
<h3 id="org9a51a22"><span class="section-number-3">4.3</span> Simple operations</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-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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> float <span class="org-tuareg-font-lock-operator">-></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">-></span> float <span class="org-tuareg-font-lock-operator">-></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">-></span> bool
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdc3ea1b" class="outline-3">
|
|
<h3 id="orgdc3ea1b"><span class="section-number-3">4.4</span> Printers</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">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">-></span> t <span class="org-tuareg-font-lock-operator">-></span> unit
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8a2e506" class="outline-2">
|
|
<h2 id="org8a2e506"><span class="section-number-2">5</span> Command line</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<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">"<string>"</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">"<int>"</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">-></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">-></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">-></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">-></span> int_of_string n
|
|
<span class="org-tuareg-font-lock-governing">in</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org73bf03e" class="outline-3">
|
|
<h3 id="org73bf03e"><span class="section-number-3">5.1</span> Types</h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml" id="org5688969"><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-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><a id="org02bac4b">Short option</a>: in the command line, a dash with a single character
|
|
(ex: <code>ls -l</code>)</li>
|
|
<li><a id="orgcd257ea">Long option</a>: 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[=<n>]</code>)</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8fc90db" class="outline-3">
|
|
<h3 id="org8fc90db"><span class="section-number-3">5.2</span> Mutable attributes</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
<p>
|
|
All the options are stored in the hash table <code>dict</code> where the key
|
|
is the <a href="#orgcd257ea">long option</a> 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">-></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">-></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">-></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">-></span> optional <span class="org-tuareg-font-lock-operator">-></span> documentation <span class="org-tuareg-font-lock-operator">-></span> description
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Function to create an anonymous argument.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7bebbc6" class="outline-3">
|
|
<h3 id="org7bebbc6"><span class="section-number-3">5.3</span> Query functions</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">get</span> <span class="org-tuareg-font-lock-operator">:</span> long_opt <span class="org-tuareg-font-lock-operator">-></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">-></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">-></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 <a href="#orgcd257ea">long option</a></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-orgd8571bd" class="outline-3">
|
|
<h3 id="orgd8571bd"><span class="section-number-3">5.4</span> Specification</h3>
|
|
<div class="outline-text-3" id="text-5-4">
|
|
<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">-></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-orge207032" class="outline-2">
|
|
<h2 id="orge207032"><span class="section-number-2">6</span> Constants</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
All constants used in the program.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org170850d" class="outline-3">
|
|
<h3 id="org170850d"><span class="section-number-3">6.1</span> Thresholds</h3>
|
|
<div class="outline-text-3" id="text-6-1">
|
|
<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 ε = 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 ε</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org03d3547" class="outline-3">
|
|
<h3 id="org03d3547"><span class="section-number-3">6.2</span> Mathematical constants</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">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-org7ed65ae" class="outline-3">
|
|
<h3 id="org7ed65ae"><span class="section-number-3">6.3</span> Physical constants</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">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-orga02825d" class="outline-2">
|
|
<h2 id="orga02825d"><span class="section-number-2">7</span> Coordinate</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<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-org365ebd1" class="outline-3">
|
|
<h3 id="org365ebd1"><span class="section-number-3">7.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-7-1">
|
|
<p>
|
|
<a id="org68c0dd2"><code>Coordinate.t</code></a>
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml" id="org0531115"><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-orgb1b5848" class="outline-3">
|
|
<h3 id="orgb1b5848"><span class="section-number-3">7.2</span> Creation</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">make</span> <span class="org-tuareg-font-lock-operator">:</span> 'a point <span class="org-tuareg-font-lock-operator">-></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">-></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-orgcb1df76" class="outline-3">
|
|
<h3 id="orgcb1df76"><span class="section-number-3">7.3</span> Conversion</h3>
|
|
<div class="outline-text-3" id="text-7-3">
|
|
<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">-></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">-></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-org4ccf2ce" class="outline-3">
|
|
<h3 id="org4ccf2ce"><span class="section-number-3">7.4</span> Vector operations</h3>
|
|
<div class="outline-text-3" id="text-7-4">
|
|
<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">-></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">-></span> bohr point <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">$| .$</td>
|
|
<td class="org-left">Scales the vector by a constant</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">\(\vert +\)</td>
|
|
<td class="org-left">Adds two vectors</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">\(\vert -\)</td>
|
|
<td class="org-left">Subtracts two vectors</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org8436887">
|
|
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-org56e65fa" class="outline-3">
|
|
<h3 id="org56e65fa"><span class="section-number-3">7.5</span> Printers</h3>
|
|
<div class="outline-text-3" id="text-7-5">
|
|
<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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></span> unit
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Coordinates can be printed in bohr or angstrom.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc46a22e" class="outline-2">
|
|
<h2 id="orgc46a22e"><span class="section-number-2">8</span> Non-negative float</h2>
|
|
<div class="outline-text-2" id="text-8">
|
|
</div>
|
|
|
|
<div id="outline-container-orgaf4f696" class="outline-3">
|
|
<h3 id="orgaf4f696"><span class="section-number-3">8.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-8-1">
|
|
<p>
|
|
<<a id="org127232a"></a>
|
|
</p>
|
|
<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-org46f8226" class="outline-3">
|
|
<h3 id="org46f8226"><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_float</span> <span class="org-tuareg-font-lock-operator">:</span> float <span class="org-tuareg-font-lock-operator">-></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">-></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">-></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">-></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">-></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-orge23858f" class="outline-2">
|
|
<h2 id="orge23858f"><span class="section-number-2">9</span> Powers</h2>
|
|
<div class="outline-text-2" id="text-9">
|
|
<p>
|
|
Contains powers of \(x\), \(y\) and \(z\) describing the polynomials in atomic basis sets.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcce21a6" class="outline-3">
|
|
<h3 id="orgcce21a6"><span class="section-number-3">9.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-9-1">
|
|
<p>
|
|
<a id="org37923cb"><code>Powers.t</code></a>
|
|
</p>
|
|
<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-orgd2a54fc" class="outline-3">
|
|
<h3 id="orgd2a54fc"><span class="section-number-3">9.2</span> Conversions</h3>
|
|
<div class="outline-text-3" id="text-9-2">
|
|
<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">-></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">-></span> int <span class="org-tuareg-font-lock-operator">*</span> int <span class="org-tuareg-font-lock-operator">*</span> int
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org5961ae9">
|
|
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-org3d41f69" class="outline-3">
|
|
<h3 id="org3d41f69"><span class="section-number-3">9.3</span> Operations</h3>
|
|
<div class="outline-text-3" id="text-9-3">
|
|
<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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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 <a href="#org37923cb"><code>Powers.t</code></a> 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 <a href="#org37923cb"><code>Powers.t</code></a> 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>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="orgc29f2cc">
|
|
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-orge1904b7" class="outline-3">
|
|
<h3 id="orge1904b7"><span class="section-number-3">9.4</span> Printers</h3>
|
|
<div class="outline-text-3" id="text-9-4">
|
|
<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">-></span> t <span class="org-tuareg-font-lock-operator">-></span> unit
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org67d3688" class="outline-2">
|
|
<h2 id="org67d3688"><span class="section-number-2">10</span> QCaml</h2>
|
|
<div class="outline-text-2" id="text-10">
|
|
<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-org604cc85" class="outline-2">
|
|
<h2 id="org604cc85"><span class="section-number-2">11</span> Range</h2>
|
|
<div class="outline-text-2" id="text-11">
|
|
<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 ; … ; 52 ; 53 ; 72 ; 73 ; … ; 106 ; 107 ; 126 ; 127 ; … ; 130 ; 131 ].</li>
|
|
</ul>
|
|
</div>
|
|
|
|
<div id="outline-container-org02778b3" class="outline-3">
|
|
<h3 id="org02778b3"><span class="section-number-3">11.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-11-1">
|
|
<p>
|
|
<a id="org2943de4"><code>Range.t</code></a>
|
|
</p>
|
|
<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-orgaa5c109" class="outline-3">
|
|
<h3 id="orgaa5c109"><span class="section-number-3">11.2</span> Conversion</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">of_string</span> <span class="org-tuareg-font-lock-operator">:</span> string <span class="org-tuareg-font-lock-operator">-></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">-></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">-></span> int list
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org936ca1b" class="outline-3">
|
|
<h3 id="org936ca1b"><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">-></span> t <span class="org-tuareg-font-lock-operator">-></span> unit
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org629a719" class="outline-2">
|
|
<h2 id="org629a719"><span class="section-number-2">12</span> Spin</h2>
|
|
<div class="outline-text-2" id="text-12">
|
|
<p>
|
|
Electron spin
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org15a9bad" class="outline-3">
|
|
<h3 id="org15a9bad"><span class="section-number-3">12.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-12-1">
|
|
<p>
|
|
<a id="orga2c23f7"><code>Spin.t</code></a>
|
|
</p>
|
|
<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-orgc66a44d" class="outline-3">
|
|
<h3 id="orgc66a44d"><span class="section-number-3">12.2</span> 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">other</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-></span> t
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Returns the opposite spin
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5ca9b50" class="outline-3">
|
|
<h3 id="org5ca9b50"><span class="section-number-3">12.3</span> Printers</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">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">-></span> t <span class="org-tuareg-font-lock-operator">-></span> unit
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9d9c2bc" class="outline-2">
|
|
<h2 id="org9d9c2bc"><span class="section-number-2">13</span> Util</h2>
|
|
<div class="outline-text-2" id="text-13">
|
|
<p>
|
|
Utility functions.
|
|
</p>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org47b536c" class="outline-3">
|
|
<h3 id="org47b536c"><span class="section-number-3">13.1</span> External C functions</h3>
|
|
<div class="outline-text-3" id="text-13-1">
|
|
<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-org733601a" class="outline-4">
|
|
<h4 id="org733601a"><span class="section-number-4">13.1.1</span> Erf</h4>
|
|
<div class="outline-text-4" id="text-13-1-1">
|
|
<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">-></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-orgab0069e" class="outline-4">
|
|
<h4 id="orgab0069e"><span class="section-number-4">13.1.2</span> Erfc</h4>
|
|
<div class="outline-text-4" id="text-13-1-2">
|
|
<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">-></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-orgd30e7a9" class="outline-4">
|
|
<h4 id="orgd30e7a9"><span class="section-number-4">13.1.3</span> Gamma</h4>
|
|
<div class="outline-text-4" id="text-13-1-3">
|
|
<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">-></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-org1b63989" class="outline-4">
|
|
<h4 id="org1b63989"><span class="section-number-4">13.1.4</span> Popcnt</h4>
|
|
<div class="outline-text-4" id="text-13-1-4">
|
|
<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">-></span> int
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdadaae7" class="outline-4">
|
|
<h4 id="orgdadaae7"><span class="section-number-4">13.1.5</span> Trailz</h4>
|
|
<div class="outline-text-4" id="text-13-1-5">
|
|
<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">-></span> int
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4fec5b6" class="outline-4">
|
|
<h4 id="org4fec5b6"><span class="section-number-4">13.1.6</span> Leadz</h4>
|
|
<div class="outline-text-4" id="text-13-1-6">
|
|
<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">-></span> int
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6af6934" class="outline-4">
|
|
<h4 id="org6af6934"><span class="section-number-4">13.1.7</span> Test</h4>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc1753fb" class="outline-3">
|
|
<h3 id="orgc1753fb"><span class="section-number-3">13.2</span> General functions</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">fact</span> <span class="org-tuareg-font-lock-operator">:</span> int <span class="org-tuareg-font-lock-operator">-></span> float
|
|
<span class="org-comment-delimiter">(* </span><span class="org-comment">@raise Invalid_argument for negative arguments or arguments >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">-></span> int <span class="org-tuareg-font-lock-operator">-></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">-></span> int <span class="org-tuareg-font-lock-operator">-></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">-></span> <span class="org-tuareg-font-lock-operator">(</span>unit <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> 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">-></span> int <span class="org-tuareg-font-lock-operator">-></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">-></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">-></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">-></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-org0e4e8b3" class="outline-3">
|
|
<h3 id="org0e4e8b3"><span class="section-number-3">13.3</span> Functions related to the Boys function</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">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">-></span> float <span class="org-tuareg-font-lock-operator">-></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">-></span> float <span class="org-tuareg-font-lock-operator">-></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-orga7ae962" class="outline-3">
|
|
<h3 id="orga7ae962"><span class="section-number-3">13.4</span> List functions</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">list_some</span> <span class="org-tuareg-font-lock-operator">:</span> 'a option list <span class="org-tuareg-font-lock-operator">-></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">-></span> int <span class="org-tuareg-font-lock-operator">-></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">-></span> 'a list <span class="org-tuareg-font-lock-operator">-></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-org5d2699c" class="outline-3">
|
|
<h3 id="org5d2699c"><span class="section-number-3">13.5</span> Array functions</h3>
|
|
<div class="outline-text-3" id="text-13-5">
|
|
<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">-></span> int <span class="org-tuareg-font-lock-operator">-></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">-></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">-></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-orgbeccc98" class="outline-3">
|
|
<h3 id="orgbeccc98"><span class="section-number-3">13.6</span> Stream functions</h3>
|
|
<div class="outline-text-3" id="text-13-6">
|
|
<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">-></span> int <span class="org-tuareg-font-lock-operator">-></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">-></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">-></span> 'b <span class="org-tuareg-font-lock-operator">-></span> 'a<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-operator">-></span> 'a <span class="org-tuareg-font-lock-operator">-></span> 'b <span class="org-tuareg-font-lock-module">Stream.</span>t <span class="org-tuareg-font-lock-operator">-></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-org2037fab" class="outline-3">
|
|
<h3 id="org2037fab"><span class="section-number-3">13.7</span> Printers</h3>
|
|
<div class="outline-text-3" id="text-13-7">
|
|
<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">-></span> float array <span class="org-tuareg-font-lock-operator">-></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">-></span> float array <span class="org-tuareg-font-lock-operator">-></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">-></span> float array array <span class="org-tuareg-font-lock-operator">-></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">-></span> float array array <span class="org-tuareg-font-lock-operator">-></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">-></span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <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">-></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>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org13d22ab">
|
|
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-org06e4fd3" class="outline-2">
|
|
<h2 id="org06e4fd3"><span class="section-number-2">14</span> Zkey</h2>
|
|
<div class="outline-text-2" id="text-14">
|
|
<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 <a href="#orga0e889d"><code>Zkey.t</code></a> 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>
|
|
|
|
<p>
|
|
Example:
|
|
</p>
|
|
<pre class="example" id="org10cb663">
|
|
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-orgee81c34" class="outline-3">
|
|
<h3 id="orgee81c34"><span class="section-number-3">14.1</span> Types</h3>
|
|
<div class="outline-text-3" id="text-14-1">
|
|
<p>
|
|
<a id="orga0e889d"><code>Zkey.t</code></a>
|
|
</p>
|
|
<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>
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|
</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-orgf60d335" class="outline-3">
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<h3 id="orgf60d335"><span class="section-number-3">14.2</span> Conversions</h3>
|
|
<div class="outline-text-3" id="text-14-2">
|
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<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">-></span> t
|
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<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">-></span> <span class="org-tuareg-font-lock-module">Powers.</span>t <span class="org-tuareg-font-lock-operator">-></span> t
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|
<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">-></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> 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">-></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> 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">-></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">-></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">-></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> 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">-></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">-></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">-></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 <a href="#org37923cb"><code>Powers.t</code></a></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>of_powers_six</code></td>
|
|
<td class="org-left">Create from two <a href="#org37923cb"><code>Powers.t</code></a></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>of_powers_nine</code></td>
|
|
<td class="org-left">Create from three <a href="#org37923cb"><code>Powers.t</code></a></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>of_powers_twelve</code></td>
|
|
<td class="org-left">Create from four <a href="#org37923cb"><code>Powers.t</code></a></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 <a href="#org37923cb"><code>Powers.t</code></a> 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-orgccdcb31" class="outline-3">
|
|
<h3 id="orgccdcb31"><span class="section-number-3">14.3</span> Functions for hash tables</h3>
|
|
<div class="outline-text-3" id="text-14-3">
|
|
<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">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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">-></span> t <span class="org-tuareg-font-lock-operator">-></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-org4f18db8" class="outline-3">
|
|
<h3 id="org4f18db8"><span class="section-number-3">14.4</span> Printers</h3>
|
|
<div class="outline-text-3" id="text-14-4">
|
|
<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">-></span> t <span class="org-tuareg-font-lock-operator">-></span> unit
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1a12374" class="outline-2">
|
|
<h2 id="org1a12374"><span class="section-number-2">15</span> Zmap</h2>
|
|
<div class="outline-text-2" id="text-15">
|
|
<p>
|
|
A hash table where the keys are <code>Zkey</code>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org2ed0818" class="outline-3">
|
|
<h3 id="org2ed0818"><span class="section-number-3">15.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-15-1">
|
|
<p>
|
|
<a id="org7aa55ee"><code>Zmap.t</code></a>
|
|
</p>
|
|
<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: 2021-01-28 Thu 00:32</p>
|
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
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</body>
|
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</html>
|