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BFraction Structure Reference
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<h1>BFraction</h1>
<div class="declaration">
<div class="language">
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">struct</span> <span class="kt">BFraction</span> <span class="p">:</span> <span class="kt">CustomStringConvertible</span><span class="p">,</span> <span class="kt">Comparable</span><span class="p">,</span> <span class="kt">Equatable</span></code></pre>
</div>
</div>
<p>A signed fraction with numerator and denominator of unbounded size.
A BFraction value is represented by a BInt numerator and a BInt denominator.
The representation is normalized, so that numerator and denominator has no common divisors except 1.
The denominator is always positive, 0 has the representation 0/1</p>
</section>
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<a name="/Constants"></a>
<a name="//apple_ref/swift/Section/Constants" class="dashAnchor"></a>
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<a class="section-name-link" href="#/Constants"></a>
<h3 class="section-name"><span>Constants</span>
</h3>
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<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV4ZEROACvpZ"></a>
<a name="//apple_ref/swift/Variable/ZERO" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV4ZEROACvpZ">ZERO</a>
</code>
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<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>BFraction(0, 1)</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="k">let</span> <span class="nv">ZERO</span><span class="p">:</span> <span class="kt">BFraction</span></code></pre>
</div>
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</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV3ONEACvpZ"></a>
<a name="//apple_ref/swift/Variable/ONE" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV3ONEACvpZ">ONE</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>BFraction(1, 1)</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="k">let</span> <span class="nv">ONE</span><span class="p">:</span> <span class="kt">BFraction</span></code></pre>
</div>
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</section>
</div>
</li>
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<a name="/Initializers"></a>
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<a class="section-name-link" href="#/Initializers"></a>
<h3 class="section-name"><span>Initializers</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionVyAcA4BIntV_AEtcfc"></a>
<a name="//apple_ref/swift/Method/init(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionVyAcA4BIntV_AEtcfc">init(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Constructs a BFraction from numerator and denominator</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Denominator is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">n</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="n">_</span> <span class="nv">d</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>n</em>
</code>
</td>
<td>
<div>
<p>The numerator</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>d</em>
</code>
</td>
<td>
<div>
<p>The denominator</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionVyAcA4BIntV_Sitcfc"></a>
<a name="//apple_ref/swift/Method/init(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionVyAcA4BIntV_Sitcfc">init(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Constructs a BFraction from numerator and denominator</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Denominator is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">n</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="n">_</span> <span class="nv">d</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>n</em>
</code>
</td>
<td>
<div>
<p>The numerator</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>d</em>
</code>
</td>
<td>
<div>
<p>The denominator</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionVyACSi_AA4BIntVtcfc"></a>
<a name="//apple_ref/swift/Method/init(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionVyACSi_AA4BIntVtcfc">init(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Constructs a BFraction from numerator and denominator</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Denominator is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="n">_</span> <span class="nv">d</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>n</em>
</code>
</td>
<td>
<div>
<p>The numerator</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>d</em>
</code>
</td>
<td>
<div>
<p>The denominator</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionVyACSi_Sitcfc"></a>
<a name="//apple_ref/swift/Method/init(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionVyACSi_Sitcfc">init(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Constructs a BFraction from numerator and denominator</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Denominator is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="n">_</span> <span class="nv">d</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>n</em>
</code>
</td>
<td>
<div>
<p>The numerator</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>d</em>
</code>
</td>
<td>
<div>
<p>The denominator</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionVyACSgSdcfc"></a>
<a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionVyACSgSdcfc">init(_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Constructs a BFraction from its decimal value</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">?(</span><span class="n">_</span> <span class="nv">d</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>d</em>
</code>
</td>
<td>
<div>
<p>The decimal value</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>The BFraction corresponding to <em>d</em>, <em>nil</em> if <em>d</em> is infinite or NaN</p>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Stored%20properties"></a>
<a name="//apple_ref/swift/Section/Stored properties" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Stored%20properties"></a>
<h3 class="section-name"><span>Stored properties</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV9numeratorAA4BIntVvp"></a>
<a name="//apple_ref/swift/Property/numerator" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV9numeratorAA4BIntVvp">numerator</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>The numerator - a BInt value</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">internal(set)</span> <span class="k">var</span> <span class="nv">numerator</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV11denominatorAA4BIntVvp"></a>
<a name="//apple_ref/swift/Property/denominator" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV11denominatorAA4BIntVvp">denominator</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>The denominator - a positive BInt value</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">internal(set)</span> <span class="k">var</span> <span class="nv">denominator</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>
</div>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Computed%20properties"></a>
<a name="//apple_ref/swift/Section/Computed properties" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Computed%20properties"></a>
<h3 class="section-name"><span>Computed properties</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV3absACvp"></a>
<a name="//apple_ref/swift/Property/abs" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV3absACvp">abs</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>The absolute value of <em>self</em></p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">abs</span><span class="p">:</span> <span class="kt">BFraction</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV11descriptionSSvp"></a>
<a name="//apple_ref/swift/Property/description" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV11descriptionSSvp">description</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>String value of <em>self</em></p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">description</span><span class="p">:</span> <span class="kt">String</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV9isIntegerSbvp"></a>
<a name="//apple_ref/swift/Property/isInteger" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV9isIntegerSbvp">isInteger</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Is <em>true</em> if <em>self</em> is an integer, that is, the denominator is 1</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">isInteger</span><span class="p">:</span> <span class="kt">Bool</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV10isNegativeSbvp"></a>
<a name="//apple_ref/swift/Property/isNegative" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV10isNegativeSbvp">isNegative</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Is <em>true</em> if <em>self</em> &lt; 0, <em>false</em> otherwise</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">isNegative</span><span class="p">:</span> <span class="kt">Bool</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV10isPositiveSbvp"></a>
<a name="//apple_ref/swift/Property/isPositive" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV10isPositiveSbvp">isPositive</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Is <em>true</em> if <em>self</em> &gt; 0, <em>false</em> otherwise</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">isPositive</span><span class="p">:</span> <span class="kt">Bool</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV6isZeroSbvp"></a>
<a name="//apple_ref/swift/Property/isZero" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV6isZeroSbvp">isZero</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Is <em>true</em> if <em>self</em> = 0, <em>false</em> otherwise</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">isZero</span><span class="p">:</span> <span class="kt">Bool</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV6signumSivp"></a>
<a name="//apple_ref/swift/Property/signum" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV6signumSivp">signum</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Is 0 if <em>self</em> = 0, 1 if <em>self</em> &gt; 0, and -1 if <em>self</em> &lt; 0</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">signum</span><span class="p">:</span> <span class="kt">Int</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>
</div>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Conversion%20functions%20to%20String%2C%20Decimal%20String%20and%20Double"></a>
<a name="//apple_ref/swift/Section/Conversion functions to String, Decimal String and Double" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Conversion%20functions%20to%20String%2C%20Decimal%20String%20and%20Double"></a>
<h3 class="section-name"><span>Conversion functions to String, Decimal String and Double</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV8asStringSSyF"></a>
<a name="//apple_ref/swift/Method/asString()" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV8asStringSSyF">asString()</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p><em>self</em> as a String</br>
Examples: BFraction(-97, 100).asString() is &ldquo;-97 / 100&rdquo;</br></p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">asString</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="kt">String</span></code></pre>
</div>
</div>
<div>
<h4>Return Value</h4>
<p><em>self</em> as a String</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV15asDecimalString6digitsSSSi_tF"></a>
<a name="//apple_ref/swift/Method/asDecimalString(digits:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV15asDecimalString6digitsSSSi_tF">asDecimalString(digits:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p><em>self</em> as a Decimal String with a given number of digits</br>
Examples: BFraction(-97, 100).asDecimalString(digits: 3) is &ldquo;-0.970&rdquo;</br>
BFraction(-97, 100).asDecimalString(digits: 0) is &ldquo;0&rdquo;</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
digits &gt;= 0
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">asDecimalString</span><span class="p">(</span><span class="nv">digits</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">String</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>digits</em>
</code>
</td>
<td>
<div>
<p>Number of digits after the decimal point</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>self</em> as a decimal String</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV8asDoubleSdyF"></a>
<a name="//apple_ref/swift/Method/asDouble()" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV8asDoubleSdyF">asDouble()</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p><em>self</em> as a Double</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">asDouble</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="kt">Double</span></code></pre>
</div>
</div>
<div>
<h4>Return Value</h4>
<p><em>self</em> as a Double or <em>Infinity</em> if <em>self</em> is not representable as a Double</p>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Addition%20functions"></a>
<a name="//apple_ref/swift/Section/Addition functions" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Addition%20functions"></a>
<h3 class="section-name"><span>Addition functions</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1popyA2CFZ"></a>
<a name="//apple_ref/swift/Method/+(_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1popyA2CFZ">+(_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Prefix plus</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="k">prefix</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>BFraction value</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1poiyA2C_ACtFZ"></a>
<a name="//apple_ref/swift/Method/+(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1poiyA2C_ACtFZ">+(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Addition</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First addend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second addend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x + y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1poiyA2C_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/+(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1poiyA2C_AA4BIntVtFZ">+(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Addition</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First addend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second addend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x + y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1poiyAcA4BIntV_ACtFZ"></a>
<a name="//apple_ref/swift/Method/+(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1poiyAcA4BIntV_ACtFZ">+(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Addition</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First addend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second addend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x + y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1poiyA2C_SitFZ"></a>
<a name="//apple_ref/swift/Method/+(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1poiyA2C_SitFZ">+(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Addition</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First addend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second addend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x + y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1poiyACSi_ACtFZ"></a>
<a name="//apple_ref/swift/Method/+(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1poiyACSi_ACtFZ">+(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Addition</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First addend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second addend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x + y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2peoiyyACz_ACtFZ"></a>
<a name="//apple_ref/swift/Method/+=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2peoiyyACz_ACtFZ">+=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x + y</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand addend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand addend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2peoiyyACz_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/+=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2peoiyyACz_AA4BIntVtFZ">+=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x + y</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand addend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand addend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2peoiyyACz_SitFZ"></a>
<a name="//apple_ref/swift/Method/+=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2peoiyyACz_SitFZ">+=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x + y</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand addend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand addend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Subtraction%20functions"></a>
<a name="//apple_ref/swift/Section/Subtraction functions" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Subtraction%20functions"></a>
<h3 class="section-name"><span>Subtraction functions</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1sopyA2CFZ"></a>
<a name="//apple_ref/swift/Method/-(_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1sopyA2CFZ">-(_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Negation</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="k">prefix</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>-x</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1soiyA2C_ACtFZ"></a>
<a name="//apple_ref/swift/Method/-(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1soiyA2C_ACtFZ">-(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Subtraction</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Minuend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Subtrahend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x - y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1soiyA2C_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/-(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1soiyA2C_AA4BIntVtFZ">-(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Subtraction</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Minuend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Subtrahend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x - y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1soiyAcA4BIntV_ACtFZ"></a>
<a name="//apple_ref/swift/Method/-(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1soiyAcA4BIntV_ACtFZ">-(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Subtraction</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Minuend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Subtrahend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x - y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1soiyA2C_SitFZ"></a>
<a name="//apple_ref/swift/Method/-(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1soiyA2C_SitFZ">-(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Subtraction</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Minuend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Subtrahend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x - y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1soiyACSi_ACtFZ"></a>
<a name="//apple_ref/swift/Method/-(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1soiyACSi_ACtFZ">-(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Subtraction</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Minuend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Subtrahend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x - y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2seoiyyACz_ACtFZ"></a>
<a name="//apple_ref/swift/Method/-=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2seoiyyACz_ACtFZ">-=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x - y</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand minuend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand subtrahend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2seoiyyACz_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/-=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2seoiyyACz_AA4BIntVtFZ">-=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x - y</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand minuend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand subtrahend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2seoiyyACz_SitFZ"></a>
<a name="//apple_ref/swift/Method/-=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2seoiyyACz_SitFZ">-=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x - y</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand minuend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand subtrahend</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Multiplication%20functions"></a>
<a name="//apple_ref/swift/Section/Multiplication functions" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Multiplication%20functions"></a>
<h3 class="section-name"><span>Multiplication functions</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1moiyA2C_ACtFZ"></a>
<a name="//apple_ref/swift/Method/*(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1moiyA2C_ACtFZ">*(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Multiplication</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">*</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Multiplier</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Multiplicand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x * y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1moiyA2C_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/*(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1moiyA2C_AA4BIntVtFZ">*(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Multiplication</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">*</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Multiplier</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Multiplicand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x * y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1moiyAcA4BIntV_ACtFZ"></a>
<a name="//apple_ref/swift/Method/*(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1moiyAcA4BIntV_ACtFZ">*(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Multiplication</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">*</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Multiplier</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Multiplicand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x * y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1moiyA2C_SitFZ"></a>
<a name="//apple_ref/swift/Method/*(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1moiyA2C_SitFZ">*(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Multiplication</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">*</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Multiplier</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Multiplicand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x * y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1moiyACSi_ACtFZ"></a>
<a name="//apple_ref/swift/Method/*(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1moiyACSi_ACtFZ">*(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Multiplication</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">*</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Multiplier</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Multiplicand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x * y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2meoiyyACz_ACtFZ"></a>
<a name="//apple_ref/swift/Method/*=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2meoiyyACz_ACtFZ">*=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x * y</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">*=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand multiplier</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand multiplicand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2meoiyyACz_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/*=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2meoiyyACz_AA4BIntVtFZ">*=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x * y</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">*=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand multiplier</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand multiplicand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2meoiyyACz_SitFZ"></a>
<a name="//apple_ref/swift/Method/*=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2meoiyyACz_SitFZ">*=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x * y</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">*=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand multiplier</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand multiplicand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Division%20functions"></a>
<a name="//apple_ref/swift/Section/Division functions" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Division%20functions"></a>
<h3 class="section-name"><span>Division functions</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1doiyA2C_ACtFZ"></a>
<a name="//apple_ref/swift/Method//(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1doiyA2C_ACtFZ">/(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Division</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Divisor is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">/</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Dividend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Divisor</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x / y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1doiyA2C_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method//(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1doiyA2C_AA4BIntVtFZ">/(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Division</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Divisor is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">/</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Dividend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Divisor</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x / y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1doiyAcA4BIntV_ACtFZ"></a>
<a name="//apple_ref/swift/Method//(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1doiyAcA4BIntV_ACtFZ">/(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Division</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Divisor is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">/</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Dividend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Divisor</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x / y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1doiyA2C_SitFZ"></a>
<a name="//apple_ref/swift/Method//(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1doiyA2C_SitFZ">/(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Division</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Divisor is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">/</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Dividend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Divisor</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x / y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1doiyACSi_ACtFZ"></a>
<a name="//apple_ref/swift/Method//(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1doiyACSi_ACtFZ">/(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Division</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Divisor is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">/</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Dividend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Divisor</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>x / y</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2deoiyyACz_ACtFZ"></a>
<a name="//apple_ref/swift/Method//=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2deoiyyACz_ACtFZ">/=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x / y</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Divisor is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">/=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand dividend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand divisor</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2deoiyyACz_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method//=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2deoiyyACz_AA4BIntVtFZ">/=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x / y</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Divisor is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">/=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand dividend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand divisor</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2deoiyyACz_SitFZ"></a>
<a name="//apple_ref/swift/Method//=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2deoiyyACz_SitFZ">/=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>x = x / y</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
Divisor is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">/=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Left hand dividend</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Right hand divisor</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV6invertACyF"></a>
<a name="//apple_ref/swift/Method/invert()" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV6invertACyF">invert()</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Invert <em>self</em></p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
<em>self</em> is not zero
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">invert</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Return Value</h4>
<p>1 / <em>self</em></p>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Exponentiation%20functions"></a>
<a name="//apple_ref/swift/Section/Exponentiation functions" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Exponentiation%20functions"></a>
<h3 class="section-name"><span>Exponentiation functions</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2mmoiyA2C_SitFZ"></a>
<a name="//apple_ref/swift/Method/**(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2mmoiyA2C_SitFZ">**(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Exponentiation</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">**</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>a</em>
</code>
</td>
<td>
<div>
<p>Operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>Exponent</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>a^x</p>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Rounding%20functions"></a>
<a name="//apple_ref/swift/Section/Rounding functions" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Rounding%20functions"></a>
<h3 class="section-name"><span>Rounding functions</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV5roundAA4BIntVyF"></a>
<a name="//apple_ref/swift/Method/round()" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV5roundAA4BIntVyF">round()</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Round</p>
<p>Returns: <em>self</em> rounded to the nearest integer</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">round</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV8truncateAA4BIntVyF"></a>
<a name="//apple_ref/swift/Method/truncate()" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV8truncateAA4BIntVyF">truncate()</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Truncate</p>
<p>Returns: <em>self</em> rounded to an integer towards 0</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">truncate</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV4ceilAA4BIntVyF"></a>
<a name="//apple_ref/swift/Method/ceil()" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV4ceilAA4BIntVyF">ceil()</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Ceil</p>
<p>Returns: <em>self</em> rounded to an integer towards +Infinity</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">ceil</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV5floorAA4BIntVyF"></a>
<a name="//apple_ref/swift/Method/floor()" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV5floorAA4BIntVyF">floor()</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Floor</p>
<p>Returns: <em>self</em> rounded to an integer towards -Infinity</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">floor</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span></code></pre>
</div>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Comparison%20functions"></a>
<a name="//apple_ref/swift/Section/Comparison functions" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Comparison%20functions"></a>
<h3 class="section-name"><span>Comparison functions</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2eeoiySbAC_ACtFZ"></a>
<a name="//apple_ref/swift/Method/==(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2eeoiySbAC_ACtFZ">==(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">==</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x = y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2eeoiySbAC_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/==(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2eeoiySbAC_AA4BIntVtFZ">==(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">==</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x = y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2eeoiySbAA4BIntV_ACtFZ"></a>
<a name="//apple_ref/swift/Method/==(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2eeoiySbAA4BIntV_ACtFZ">==(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">==</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x = y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2eeoiySbAC_SitFZ"></a>
<a name="//apple_ref/swift/Method/==(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2eeoiySbAC_SitFZ">==(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">==</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x = y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2eeoiySbSi_ACtFZ"></a>
<a name="//apple_ref/swift/Method/==(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2eeoiySbSi_ACtFZ">==(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">==</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x = y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2neoiySbAC_ACtFZ"></a>
<a name="//apple_ref/swift/Method/!=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2neoiySbAC_ACtFZ">!=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Not equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">!=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x != y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2neoiySbAC_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/!=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2neoiySbAC_AA4BIntVtFZ">!=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Not equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">!=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x != y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2neoiySbAA4BIntV_ACtFZ"></a>
<a name="//apple_ref/swift/Method/!=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2neoiySbAA4BIntV_ACtFZ">!=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Not equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">!=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x != y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2neoiySbAC_SitFZ"></a>
<a name="//apple_ref/swift/Method/!=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2neoiySbAC_SitFZ">!=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Not equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">!=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x != y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2neoiySbSi_ACtFZ"></a>
<a name="//apple_ref/swift/Method/!=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2neoiySbSi_ACtFZ">!=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Not equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">!=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x != y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1loiySbAC_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&lt;(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1loiySbAC_ACtFZ"><(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Less than</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &lt; y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1loiySbAC_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/&lt;(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1loiySbAC_AA4BIntVtFZ"><(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Less than</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &lt; y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1loiySbAA4BIntV_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&lt;(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1loiySbAA4BIntV_ACtFZ"><(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Less than</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &lt; y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1loiySbAC_SitFZ"></a>
<a name="//apple_ref/swift/Method/&lt;(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1loiySbAC_SitFZ"><(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Less than</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &lt; y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1loiySbSi_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&lt;(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1loiySbSi_ACtFZ"><(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Less than</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &lt; y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1goiySbAC_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&gt;(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1goiySbAC_ACtFZ">>(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Greater than</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &gt; y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1goiySbAC_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/&gt;(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1goiySbAC_AA4BIntVtFZ">>(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Greater than</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &gt; y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1goiySbAA4BIntV_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&gt;(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1goiySbAA4BIntV_ACtFZ">>(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Greater than</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &gt; y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1goiySbAC_SitFZ"></a>
<a name="//apple_ref/swift/Method/&gt;(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1goiySbAC_SitFZ">>(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Greater than</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &gt; y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV1goiySbSi_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&gt;(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV1goiySbSi_ACtFZ">>(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Greater than</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &gt; y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2leoiySbAC_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&lt;=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2leoiySbAC_ACtFZ"><=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Less than or equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &lt;= y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2leoiySbAC_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/&lt;=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2leoiySbAC_AA4BIntVtFZ"><=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Less than or equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &lt;= y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2leoiySbAA4BIntV_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&lt;=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2leoiySbAA4BIntV_ACtFZ"><=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Less than or equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &lt;= y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2leoiySbAC_SitFZ"></a>
<a name="//apple_ref/swift/Method/&lt;=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2leoiySbAC_SitFZ"><=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Less than or equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &lt;= y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2leoiySbSi_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&lt;=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2leoiySbSi_ACtFZ"><=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Less than or equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &lt;= y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2geoiySbAC_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&gt;=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2geoiySbAC_ACtFZ">>=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Greater than or equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &gt;= y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2geoiySbAC_AA4BIntVtFZ"></a>
<a name="//apple_ref/swift/Method/&gt;=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2geoiySbAC_AA4BIntVtFZ">>=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Greater than or equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &gt;= y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2geoiySbAA4BIntV_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&gt;=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2geoiySbAA4BIntV_ACtFZ">>=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Greater than or equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="../Structs/BInt.html">BInt</a></span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &gt;= y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2geoiySbAC_SitFZ"></a>
<a name="//apple_ref/swift/Method/&gt;=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2geoiySbAC_SitFZ">>=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Greater than or equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &gt;= y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV2geoiySbSi_ACtFZ"></a>
<a name="//apple_ref/swift/Method/&gt;=(_:_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV2geoiySbSi_ACtFZ">>=(_:<wbr>_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Greater than or equal</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;=</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BFraction</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>x</em>
</code>
</td>
<td>
<div>
<p>First operand</p>
</div>
</td>
</tr>
<tr>
<td>
<code>
<em>y</em>
</code>
</td>
<td>
<div>
<p>Second operand</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p><em>true</em> if x &gt;= y, <em>false</em> otherwise</p>
</div>
</section>
</div>
</li>
</ul>
</div>
<div class="task-group">
<div class="task-name-container">
<a name="/Miscellaneous%20functions"></a>
<a name="//apple_ref/swift/Section/Miscellaneous functions" class="dashAnchor"></a>
<div class="section-name-container">
<a class="section-name-link" href="#/Miscellaneous%20functions"></a>
<h3 class="section-name"><span>Miscellaneous functions</span>
</h3>
</div>
</div>
<ul>
<li class="item">
<div>
<code>
<a name="/s:6BigInt9BFractionV9bernoulliyACSiFZ"></a>
<a name="//apple_ref/swift/Method/bernoulli(_:)" class="dashAnchor"></a>
<a class="token" href="#/s:6BigInt9BFractionV9bernoulliyACSiFZ">bernoulli(_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Bernoulli numbers</p>
<div class="aside aside-precondition">
<p class="aside-title">Precondition</p>
n &gt;= 0
</div>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">bernoulli</span><span class="p">(</span><span class="n">_</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BFraction</span></code></pre>
</div>
</div>
<div>
<h4>Parameters</h4>
<table class="graybox">
<tbody>
<tr>
<td>
<code>
<em>n</em>
</code>
</td>
<td>
<div>
<p>The Bernoulli index</p>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h4>Return Value</h4>
<p>The n&#39;th Bernoulli number</p>
</div>
</section>
</div>
</li>
</ul>
</div>
</section>
</section>
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