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<h1 class="title">std/rationals</h1>
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<a class="reference reference-toplevel" href="#6" id="56">Imports</a>
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<details open>
<summary><a class="reference reference-toplevel" href="#7" id="57">Types</a></summary>
<ul class="simple simple-toc-section">
<li><a class="reference" href="#Rational" title="Rational[T] = object
num*, den*: T">Rational</a></li>
</ul>
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<details open>
<summary><a class="reference reference-toplevel" href="#12" id="62">Procs</a></summary>
<ul class="simple simple-toc-section">
<ul class="simple nested-toc-section">$
<li><a class="reference" href="#%24%2CRational%5BT%5D" title="`$`[T](x: Rational[T]): string">`$`[T](x: Rational[T]): string</a></li>
</ul>
<ul class="simple nested-toc-section">*
<li><a class="reference" href="#%2A%2CRational%5BT%5D%2CRational%5BT%5D" title="`*`[T](x, y: Rational[T]): Rational[T]">`*`[T](x, y: Rational[T]): Rational[T]</a></li>
<li><a class="reference" href="#%2A%2CRational%5BT%5D%2CT" title="`*`[T](x: Rational[T]; y: T): Rational[T]">`*`[T](x: Rational[T]; y: T): Rational[T]</a></li>
<li><a class="reference" href="#%2A%2CT%2CRational%5BT%5D" title="`*`[T](x: T; y: Rational[T]): Rational[T]">`*`[T](x: T; y: Rational[T]): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">*=
<li><a class="reference" href="#%2A%3D%2CRational%5BT%5D%2CRational%5BT%5D" title="`*=`[T](x: var Rational[T]; y: Rational[T])">`*=`[T](x: var Rational[T]; y: Rational[T])</a></li>
<li><a class="reference" href="#%2A%3D%2CRational%5BT%5D%2CT" title="`*=`[T](x: var Rational[T]; y: T)">`*=`[T](x: var Rational[T]; y: T)</a></li>
</ul>
<ul class="simple nested-toc-section">+
<li><a class="reference" href="#%2B%2CRational%5BT%5D%2CRational%5BT%5D" title="`+`[T](x, y: Rational[T]): Rational[T]">`+`[T](x, y: Rational[T]): Rational[T]</a></li>
<li><a class="reference" href="#%2B%2CRational%5BT%5D%2CT" title="`+`[T](x: Rational[T]; y: T): Rational[T]">`+`[T](x: Rational[T]; y: T): Rational[T]</a></li>
<li><a class="reference" href="#%2B%2CT%2CRational%5BT%5D" title="`+`[T](x: T; y: Rational[T]): Rational[T]">`+`[T](x: T; y: Rational[T]): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">+=
<li><a class="reference" href="#%2B%3D%2CRational%5BT%5D%2CRational%5BT%5D" title="`+=`[T](x: var Rational[T]; y: Rational[T])">`+=`[T](x: var Rational[T]; y: Rational[T])</a></li>
<li><a class="reference" href="#%2B%3D%2CRational%5BT%5D%2CT" title="`+=`[T](x: var Rational[T]; y: T)">`+=`[T](x: var Rational[T]; y: T)</a></li>
</ul>
<ul class="simple nested-toc-section">-
<li><a class="reference" href="#-%2CRational%5BT%5D%2CRational%5BT%5D" title="`-`[T](x, y: Rational[T]): Rational[T]">`-`[T](x, y: Rational[T]): Rational[T]</a></li>
<li><a class="reference" href="#-%2CRational%5BT%5D" title="`-`[T](x: Rational[T]): Rational[T]">`-`[T](x: Rational[T]): Rational[T]</a></li>
<li><a class="reference" href="#-%2CRational%5BT%5D%2CT" title="`-`[T](x: Rational[T]; y: T): Rational[T]">`-`[T](x: Rational[T]; y: T): Rational[T]</a></li>
<li><a class="reference" href="#-%2CT%2CRational%5BT%5D" title="`-`[T](x: T; y: Rational[T]): Rational[T]">`-`[T](x: T; y: Rational[T]): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">-=
<li><a class="reference" href="#-%3D%2CRational%5BT%5D%2CRational%5BT%5D" title="`-=`[T](x: var Rational[T]; y: Rational[T])">`-=`[T](x: var Rational[T]; y: Rational[T])</a></li>
<li><a class="reference" href="#-%3D%2CRational%5BT%5D%2CT" title="`-=`[T](x: var Rational[T]; y: T)">`-=`[T](x: var Rational[T]; y: T)</a></li>
</ul>
<ul class="simple nested-toc-section">/
<li><a class="reference" href="#%2F%2CRational%5BT%5D%2CRational%5BT%5D" title="`/`[T](x, y: Rational[T]): Rational[T]">`/`[T](x, y: Rational[T]): Rational[T]</a></li>
<li><a class="reference" href="#%2F%2CRational%5BT%5D%2CT" title="`/`[T](x: Rational[T]; y: T): Rational[T]">`/`[T](x: Rational[T]; y: T): Rational[T]</a></li>
<li><a class="reference" href="#%2F%2CT%2CRational%5BT%5D" title="`/`[T](x: T; y: Rational[T]): Rational[T]">`/`[T](x: T; y: Rational[T]): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">//
<li><a class="reference" href="#%2F%2F%2CT%2CT" title="`//`[T](num, den: T): Rational[T]">`//`[T](num, den: T): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">/=
<li><a class="reference" href="#%2F%3D%2CRational%5BT%5D%2CRational%5BT%5D" title="`/=`[T](x: var Rational[T]; y: Rational[T])">`/=`[T](x: var Rational[T]; y: Rational[T])</a></li>
<li><a class="reference" href="#%2F%3D%2CRational%5BT%5D%2CT" title="`/=`[T](x: var Rational[T]; y: T)">`/=`[T](x: var Rational[T]; y: T)</a></li>
</ul>
<ul class="simple nested-toc-section"><
<li><a class="reference" href="#%3C%2CRational%2CRational" title="`&lt;`(x, y: Rational): bool">`&lt;`(x, y: Rational): bool</a></li>
</ul>
<ul class="simple nested-toc-section"><=
<li><a class="reference" href="#%3C%3D%2CRational%2CRational" title="`&lt;=`(x, y: Rational): bool">`&lt;=`(x, y: Rational): bool</a></li>
</ul>
<ul class="simple nested-toc-section">==
<li><a class="reference" href="#%3D%3D%2CRational%2CRational" title="`==`(x, y: Rational): bool">`==`(x, y: Rational): bool</a></li>
</ul>
<ul class="simple nested-toc-section">^
<li><a class="reference" href="#%5E%2CRational%5BT%3A%20SomeInteger%5D%2CT" title="`^`[T: SomeInteger](x: Rational[T]; y: T): Rational[T]">`^`[T: SomeInteger](x: Rational[T]; y: T): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">abs
<li><a class="reference" href="#abs%2CRational%5BT%5D" title="abs[T](x: Rational[T]): Rational[T]">abs[T](x: Rational[T]): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">cmp
<li><a class="reference" href="#cmp%2CRational%2CRational" title="cmp(x, y: Rational): int">cmp(x, y: Rational): int</a></li>
</ul>
<ul class="simple nested-toc-section">div
<li><a class="reference" href="#div%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D" title="`div`[T: SomeInteger](x, y: Rational[T]): T">`div`[T: SomeInteger](x, y: Rational[T]): T</a></li>
</ul>
<ul class="simple nested-toc-section">floorDiv
<li><a class="reference" href="#floorDiv%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D" title="floorDiv[T: SomeInteger](x, y: Rational[T]): T">floorDiv[T: SomeInteger](x, y: Rational[T]): T</a></li>
</ul>
<ul class="simple nested-toc-section">floorMod
<li><a class="reference" href="#floorMod%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D" title="floorMod[T: SomeInteger](x, y: Rational[T]): Rational[T]">floorMod[T: SomeInteger](x, y: Rational[T]): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">hash
<li><a class="reference" href="#hash%2CRational%5BT%5D" title="hash[T](x: Rational[T]): Hash">hash[T](x: Rational[T]): Hash</a></li>
</ul>
<ul class="simple nested-toc-section">initRational
<li><a class="reference" href="#initRational%2CT%2CT" title="initRational[T: SomeInteger](num, den: T): Rational[T]">initRational[T: SomeInteger](num, den: T): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">mod
<li><a class="reference" href="#mod%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D" title="`mod`[T: SomeInteger](x, y: Rational[T]): Rational[T]">`mod`[T: SomeInteger](x, y: Rational[T]): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">reciprocal
<li><a class="reference" href="#reciprocal%2CRational%5BT%5D" title="reciprocal[T](x: Rational[T]): Rational[T]">reciprocal[T](x: Rational[T]): Rational[T]</a></li>
</ul>
<ul class="simple nested-toc-section">reduce
<li><a class="reference" href="#reduce%2CRational%5BT%3A%20SomeInteger%5D" title="reduce[T: SomeInteger](x: var Rational[T])">reduce[T: SomeInteger](x: var Rational[T])</a></li>
</ul>
<ul class="simple nested-toc-section">toFloat
<li><a class="reference" href="#toFloat%2CRational%5BT%5D" title="toFloat[T](x: Rational[T]): float">toFloat[T](x: Rational[T]): float</a></li>
</ul>
<ul class="simple nested-toc-section">toInt
<li><a class="reference" href="#toInt%2CRational%5BT%5D" title="toInt[T](x: Rational[T]): int">toInt[T](x: Rational[T]): int</a></li>
</ul>
<ul class="simple nested-toc-section">toRational
<li><a class="reference" href="#toRational%2Cfloat%2Cint" title="toRational(x: float; n: int = high(int) shr 32): Rational[int]">toRational(x: float; n: int = high(int) shr 32): Rational[int]</a></li>
<li><a class="reference" href="#toRational%2CT" title="toRational[T: SomeInteger](x: T): Rational[T]">toRational[T: SomeInteger](x: T): Rational[T]</a></li>
</ul>
</ul>
</details>
</li>
</ul>
</div>
<div class="nine columns" id="content">
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L1" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L1" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
<div id="tocRoot"></div>
<p class="module-desc">This module implements rational numbers, consisting of a numerator and a denominator. The denominator can not be 0.
<p><strong class="examples_text">Example:</strong></p>
<pre class="listing"><span class="Keyword">import</span> <span class="Identifier">std</span><span class="Operator">/</span><span class="Identifier">rationals</span>
<span class="Keyword">let</span>
<span class="Identifier">r1</span> <span class="Operator">=</span> <span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span>
<span class="Identifier">r2</span> <span class="Operator">=</span> <span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">4</span>
<span class="Identifier">doAssert</span> <span class="Identifier">r1</span> <span class="Operator">+</span> <span class="Identifier">r2</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">4</span>
<span class="Identifier">doAssert</span> <span class="Identifier">r1</span> <span class="Operator">-</span> <span class="Identifier">r2</span> <span class="Operator">==</span> <span class="DecNumber">5</span> <span class="Operator">//</span> <span class="DecNumber">4</span>
<span class="Identifier">doAssert</span> <span class="Identifier">r1</span> <span class="Operator">*</span> <span class="Identifier">r2</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">8</span>
<span class="Identifier">doAssert</span> <span class="Identifier">r1</span> <span class="Operator">/</span> <span class="Identifier">r2</span> <span class="Operator">==</span> <span class="Operator">-</span><span class="DecNumber">2</span> <span class="Operator">//</span> <span class="DecNumber">3</span></pre></p>
<div class="section" id="6">
<h1><a class="toc-backref" href="#6">Imports</a></h1>
<dl class="item">
<a class="reference external" href="math.html">math</a>, <a class="reference external" href="hashes.html">hashes</a>, <a class="reference external" href="assertions.html">assertions</a>
</dl>
</div>
<div class="section" id="7">
<h1><a class="toc-backref" href="#7">Types</a></h1>
<dl class="item">
<div id="Rational">
<dt><pre><a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span> <span class="Other">=</span> <span class="Keyword">object</span>
<span class="Identifier">num</span><span class="Operator">*</span><span class="Other">,</span> <span class="Identifier">den</span><span class="Operator">*</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
<dd>
A rational number, consisting of a numerator <tt class="docutils literal"><span class="pre"><span class="Identifier">num</span></span></tt> and a denominator <tt class="docutils literal"><span class="pre"><span class="Identifier">den</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L28" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L28" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</dl>
</div>
<div class="section" id="12">
<h1><a class="toc-backref" href="#12">Procs</a></h1>
<dl class="item">
<div id="$-procs-all">
<div id="$,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#%24%2CRational%5BT%5D"><span class="Identifier">`$`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#string"><span class="Identifier">string</span></a></pre></dt>
<dd>
Turns a rational number into a string.
<p><strong class="examples_text">Example:</strong></p>
<pre class="listing"><span class="Identifier">doAssert</span> <span class="Operator">$</span><span class="Punctuation">(</span><span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="StringLit">&quot;1/2&quot;</span></pre>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L71" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L71" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="*-procs-all">
<div id="*,Rational[T],Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#%2A%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Multiplies two rational numbers.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L180" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L180" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="*,Rational[T],T">
<dt><pre><span class="Keyword">func</span> <a href="#%2A%2CRational%5BT%5D%2CT"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Multiplies the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> with the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L185" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L185" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="*,T,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#%2A%2CT%2CRational%5BT%5D"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Multiplies the int <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> with the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L190" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L190" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="*=-procs-all">
<div id="*=,Rational[T],Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#%2A%3D%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`*=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
<dd>
Multiplies the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> in-place.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L195" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L195" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="*=,Rational[T],T">
<dt><pre><span class="Keyword">func</span> <a href="#%2A%3D%2CRational%5BT%5D%2CT"><span class="Identifier">`*=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span></pre></dt>
<dd>
Multiplies the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> in-place.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L201" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L201" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="+-procs-all">
<div id="+,Rational[T],Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#%2B%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Adds two rational numbers.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L122" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L122" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="+,Rational[T],T">
<dt><pre><span class="Keyword">func</span> <a href="#%2B%2CRational%5BT%5D%2CT"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Adds the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L130" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L130" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="+,T,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#%2B%2CT%2CRational%5BT%5D"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Adds the int <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L134" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L134" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="+=-procs-all">
<div id="+=,Rational[T],Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#%2B%3D%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`+=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
<dd>
Adds the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> to the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> in-place.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L138" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L138" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="+=,Rational[T],T">
<dt><pre><span class="Keyword">func</span> <a href="#%2B%3D%2CRational%5BT%5D%2CT"><span class="Identifier">`+=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span></pre></dt>
<dd>
Adds the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> to the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> in-place.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L145" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L145" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="--procs-all">
<div id="-,Rational[T],Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#-%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Subtracts two rational numbers.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L153" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L153" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="-,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#-%2CRational%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Unary minus for rational numbers.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L149" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L149" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="-,Rational[T],T">
<dt><pre><span class="Keyword">func</span> <a href="#-%2CRational%5BT%5D%2CT"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Subtracts the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> from the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L161" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L161" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="-,T,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#-%2CT%2CRational%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Subtracts the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> from the int <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L165" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L165" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="-=-procs-all">
<div id="-=,Rational[T],Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#-%3D%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`-=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
<dd>
Subtracts the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> from the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> in-place.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L169" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L169" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="-=,Rational[T],T">
<dt><pre><span class="Keyword">func</span> <a href="#-%3D%2CRational%5BT%5D%2CT"><span class="Identifier">`-=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span></pre></dt>
<dd>
Subtracts the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> from the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> in-place.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L176" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L176" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="/-procs-all">
<div id="/,Rational[T],Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#%2F%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Divides the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L216" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L216" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="/,Rational[T],T">
<dt><pre><span class="Keyword">func</span> <a href="#%2F%2CRational%5BT%5D%2CT"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Divides the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L221" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L221" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="/,T,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#%2F%2CT%2CRational%5BT%5D"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Divides the int <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L226" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L226" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="//-procs-all">
<div id="//,T,T">
<dt><pre><span class="Keyword">func</span> <a href="#%2F%2F%2CT%2CT"><span class="Identifier">`//`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">num</span><span class="Other">,</span> <span class="Identifier">den</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
A friendlier version of <a class="reference external" href="#initRational,T,T">initRational</a>.
<p><strong class="examples_text">Example:</strong></p>
<pre class="listing"><span class="Keyword">let</span> <span class="Identifier">x</span> <span class="Operator">=</span> <span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">3</span> <span class="Operator">+</span> <span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">5</span>
<span class="Identifier">doAssert</span> <span class="Identifier">x</span> <span class="Operator">==</span> <span class="DecNumber">8</span> <span class="Operator">//</span> <span class="DecNumber">15</span></pre>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L63" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L63" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="/=-procs-all">
<div id="/=,Rational[T],Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#%2F%3D%2CRational%5BT%5D%2CRational%5BT%5D"><span class="Identifier">`/=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
<dd>
Divides the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> in-place.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L231" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L231" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="/=,Rational[T],T">
<dt><pre><span class="Keyword">func</span> <a href="#%2F%3D%2CRational%5BT%5D%2CT"><span class="Identifier">`/=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span></pre></dt>
<dd>
Divides the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by the int <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> in-place.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L237" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L237" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="&lt;-procs-all">
<div id="<,Rational,Rational">
<dt><pre><span class="Keyword">func</span> <a href="#%3C%2CRational%2CRational"><span class="Identifier">`&lt;`</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a></pre></dt>
<dd>
Returns true if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is less than <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L249" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L249" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="&lt;=-procs-all">
<div id="<=,Rational,Rational">
<dt><pre><span class="Keyword">func</span> <a href="#%3C%3D%2CRational%2CRational"><span class="Identifier">`&lt;=`</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a></pre></dt>
<dd>
Returns tue if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is less than or equal to <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L253" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L253" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="==-procs-all">
<div id="==,Rational,Rational">
<dt><pre><span class="Keyword">func</span> <a href="#%3D%3D%2CRational%2CRational"><span class="Identifier">`==`</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a></pre></dt>
<dd>
Compares two rationals for equality.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L257" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L257" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="^-procs-all">
<div id="^,Rational[T: SomeInteger],T">
<dt><pre><span class="Keyword">func</span> <a href="#%5E%2CRational%5BT%3A%20SomeInteger%5D%2CT"><span class="Identifier">`^`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
<p>Computes <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to the power of <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.</p>
<p>The exponent <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> must be an integer. Negative exponents are supported but floating point exponents are not.</p>
<p><strong class="examples_text">Example:</strong></p>
<pre class="listing"><span class="Identifier">doAssert</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">^</span> <span class="DecNumber">0</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">1</span><span class="Punctuation">)</span>
<span class="Identifier">doAssert</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">^</span> <span class="DecNumber">1</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">5</span><span class="Punctuation">)</span>
<span class="Identifier">doAssert</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">^</span> <span class="DecNumber">2</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="DecNumber">9</span> <span class="Operator">//</span> <span class="DecNumber">25</span><span class="Punctuation">)</span>
<span class="Identifier">doAssert</span> <span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">3</span> <span class="Operator">//</span> <span class="DecNumber">5</span><span class="Punctuation">)</span> <span class="Operator">^</span> <span class="Operator">-</span><span class="DecNumber">2</span> <span class="Operator">==</span> <span class="Punctuation">(</span><span class="DecNumber">25</span> <span class="Operator">//</span> <span class="DecNumber">9</span><span class="Punctuation">)</span></pre>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L307" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L307" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="abs-procs-all">
<div id="abs,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#abs%2CRational%5BT%5D"><span class="Identifier">abs</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Returns the absolute value of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
<p><strong class="examples_text">Example:</strong></p>
<pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">abs</span><span class="Punctuation">(</span><span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span>
<span class="Identifier">doAssert</span> <span class="Identifier">abs</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">1</span> <span class="Operator">//</span> <span class="DecNumber">2</span></pre>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L261" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L261" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="cmp-procs-all">
<div id="cmp,Rational,Rational">
<dt><pre><span class="Keyword">func</span> <a href="#cmp%2CRational%2CRational"><span class="Identifier">cmp</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a></pre></dt>
<dd>
Compares two rationals. Returns<ul class="simple"><li>a value less than zero, if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">&lt;</span> <span class="Identifier">y</span></span></tt></li>
<li>a value greater than zero, if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">&gt;</span> <span class="Identifier">y</span></span></tt></li>
<li>zero, if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">==</span> <span class="Identifier">y</span></span></tt></li>
</ul>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L242" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L242" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="div-procs-all">
<div id="div,Rational[T: SomeInteger],Rational[T: SomeInteger]">
<dt><pre><span class="Keyword">func</span> <a href="#div%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D"><span class="Identifier">`div`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
<dd>
Computes the rational truncated division.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L268" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L268" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="floorDiv-procs-all">
<div id="floorDiv,Rational[T: SomeInteger],Rational[T: SomeInteger]">
<dt><pre><span class="Keyword">func</span> <a href="#floorDiv%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D"><span class="Identifier">floorDiv</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
<dd>
<p>Computes the rational floor division.</p>
<p>Floor division is conceptually defined as <tt class="docutils literal"><span class="pre"><span class="Identifier">floor</span><span class="Punctuation">(</span><span class="Identifier">x</span> <span class="Operator">/</span> <span class="Identifier">y</span><span class="Punctuation">)</span></span></tt>. This is different from the <tt class="docutils literal"><span class="pre"><span class="Keyword">div</span></span></tt> operator, which is defined as <tt class="docutils literal"><span class="pre"><span class="Identifier">trunc</span><span class="Punctuation">(</span><span class="Identifier">x</span> <span class="Operator">/</span> <span class="Identifier">y</span><span class="Punctuation">)</span></span></tt>. That is, <tt class="docutils literal"><span class="pre"><span class="Keyword">div</span></span></tt> rounds towards 0 and <tt class="docutils literal"><span class="pre"><span class="Identifier">floorDiv</span></span></tt> rounds down.</p>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L278" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L278" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="floorMod-procs-all">
<div id="floorMod,Rational[T: SomeInteger],Rational[T: SomeInteger]">
<dt><pre><span class="Keyword">func</span> <a href="#floorMod%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D"><span class="Identifier">floorMod</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
<p>Computes the rational modulo by floor division (modulo).</p>
<p>This is same as <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">-</span> <span class="Identifier">floorDiv</span><span class="Punctuation">(</span><span class="Identifier">x</span><span class="Punctuation">,</span> <span class="Identifier">y</span><span class="Punctuation">)</span> <span class="Operator">*</span> <span class="Identifier">y</span></span></tt>. This func behaves the same as the <tt class="docutils literal"><span class="pre"><span class="Operator">%</span></span></tt> operator in Python.</p>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L287" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L287" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="hash-procs-all">
<div id="hash,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#hash%2CRational%5BT%5D"><span class="Identifier">hash</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="hashes.html#Hash"><span class="Identifier">Hash</span></a></pre></dt>
<dd>
Computes the hash for the rational <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L295" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L295" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="initRational-procs-all">
<div id="initRational,T,T">
<dt><pre><span class="Keyword">func</span> <a href="#initRational%2CT%2CT"><span class="Identifier">initRational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">num</span><span class="Other">,</span> <span class="Identifier">den</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
<p>Creates a new rational number with numerator <tt class="docutils literal"><span class="pre"><span class="Identifier">num</span></span></tt> and denominator <tt class="docutils literal"><span class="pre"><span class="Identifier">den</span></span></tt>. <tt class="docutils literal"><span class="pre"><span class="Identifier">den</span></span></tt> must not be 0.</p>
<p><strong>Note:</strong> <tt class="docutils literal"><span class="pre"><span class="Identifier">den</span> <span class="Operator">!=</span> <span class="DecNumber">0</span></span></tt> is not checked when assertions are turned off.</p>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L54" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L54" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="mod-procs-all">
<div id="mod,Rational[T: SomeInteger],Rational[T: SomeInteger]">
<dt><pre><span class="Keyword">func</span> <a href="#mod%2CRational%5BT%3A%20SomeInteger%5D%2CRational%5BT%3A%20SomeInteger%5D"><span class="Identifier">`mod`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Computes the rational modulo by truncated division (remainder). This is same as <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span> <span class="Operator">-</span> <span class="Punctuation">(</span><span class="Identifier">x</span> <span class="Keyword">div</span> <span class="Identifier">y</span><span class="Punctuation">)</span> <span class="Operator">*</span> <span class="Identifier">y</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L272" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L272" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="reciprocal-procs-all">
<div id="reciprocal,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#reciprocal%2CRational%5BT%5D"><span class="Identifier">reciprocal</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Calculates the reciprocal of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="DecNumber">1</span><span class="Operator">/</span><span class="Identifier">x</span></span></tt>). If <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is 0, raises <tt class="docutils literal"><span class="pre"><span class="Identifier">DivByZeroDefect</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L206" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L206" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="reduce-procs-all">
<div id="reduce,Rational[T: SomeInteger]">
<dt><pre><span class="Keyword">func</span> <a href="#reduce%2CRational%5BT%3A%20SomeInteger%5D"><span class="Identifier">reduce</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
<dd>
<p>Reduces the rational number <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>, so that the numerator and denominator have no common divisors other than 1 (and -1). If <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> is 0, raises <tt class="docutils literal"><span class="pre"><span class="Identifier">DivByZeroDefect</span></span></tt>.</p>
<p><strong>Note:</strong> This is called automatically by the various operations on rationals.</p>
<p><strong class="examples_text">Example:</strong></p>
<pre class="listing"><span class="Keyword">var</span> <span class="Identifier">r</span> <span class="Operator">=</span> <span class="Identifier">Rational</span><span class="Punctuation">[</span><span class="Identifier">int</span><span class="Punctuation">]</span><span class="Punctuation">(</span><span class="Identifier">num</span><span class="Punctuation">:</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="Identifier">den</span><span class="Punctuation">:</span> <span class="DecNumber">4</span><span class="Punctuation">)</span> <span class="Comment"># 1/2</span>
<span class="Identifier">reduce</span><span class="Punctuation">(</span><span class="Identifier">r</span><span class="Punctuation">)</span>
<span class="Identifier">doAssert</span> <span class="Identifier">r</span><span class="Operator">.</span><span class="Identifier">num</span> <span class="Operator">==</span> <span class="DecNumber">1</span>
<span class="Identifier">doAssert</span> <span class="Identifier">r</span><span class="Operator">.</span><span class="Identifier">den</span> <span class="Operator">==</span> <span class="DecNumber">2</span></pre>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L32" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L32" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="toFloat-procs-all">
<div id="toFloat,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#toFloat%2CRational%5BT%5D"><span class="Identifier">toFloat</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#float"><span class="Identifier">float</span></a></pre></dt>
<dd>
Converts a rational number <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to a <tt class="docutils literal"><span class="pre"><span class="Identifier">float</span></span></tt>.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L113" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L113" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="toInt-procs-all">
<div id="toInt,Rational[T]">
<dt><pre><span class="Keyword">func</span> <a href="#toInt%2CRational%5BT%5D"><span class="Identifier">toInt</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a></pre></dt>
<dd>
Converts a rational number <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to an <tt class="docutils literal"><span class="pre"><span class="Identifier">int</span></span></tt>. Conversion rounds towards 0 if <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> does not contain an integer value.
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L117" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L117" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
</div>
<div id="toRational-procs-all">
<div id="toRational,float,int">
<dt><pre><span class="Keyword">func</span> <a href="#toRational%2Cfloat%2Cint"><span class="Identifier">toRational</span></a><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="system.html#float"><span class="Identifier">float</span></a><span class="Other">;</span> <span class="Identifier">n</span><span class="Other">:</span> <a href="system.html#int"><span class="Identifier">int</span></a> <span class="Other">=</span> <span class="Identifier">high</span><span class="Other">(</span><a href="system.html#int"><span class="Identifier">int</span></a><span class="Other">)</span> <span class="Keyword">shr</span> <span class="DecNumber">32</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><a href="system.html#int"><span class="Identifier">int</span></a><span class="Other">]</span> {.
<span><span class="Other pragmadots">...</span></span><span class="pragmawrap"><span class="Identifier">raises</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span> <span class="Identifier">tags</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span> <span class="Identifier">forbids</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span></span>.}</pre></dt>
<dd>
<p>Calculates the best rational approximation of <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>, where the denominator is smaller than <tt class="docutils literal"><span class="pre"><span class="Identifier">n</span></span></tt> (default is the largest possible <tt class="docutils literal"><span class="pre"><span class="Identifier">int</span></span></tt> for maximal resolution).</p>
<p>The algorithm is based on the theory of continued fractions.</p>
<p><strong class="examples_text">Example:</strong></p>
<pre class="listing"><span class="Keyword">let</span> <span class="Identifier">x</span> <span class="Operator">=</span> <span class="FloatNumber">1.2</span>
<span class="Identifier">doAssert</span> <span class="Identifier">x</span><span class="Operator">.</span><span class="Identifier">toRational</span><span class="Operator">.</span><span class="Identifier">toFloat</span> <span class="Operator">==</span> <span class="Identifier">x</span></pre>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L84" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L84" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
<div id="toRational,T">
<dt><pre><span class="Keyword">func</span> <a href="#toRational%2CT"><span class="Identifier">toRational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeInteger"><span class="Identifier">SomeInteger</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="rationals.html#Rational"><span class="Identifier">Rational</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
<dd>
Converts some integer <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> to a rational number.
<p><strong class="examples_text">Example:</strong></p>
<pre class="listing"><span class="Identifier">doAssert</span> <span class="Identifier">toRational</span><span class="Punctuation">(</span><span class="DecNumber">42</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="DecNumber">42</span> <span class="Operator">//</span> <span class="DecNumber">1</span></pre>
<a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/rationals.nim#L78" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/rationals.nim#L78" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
</dd>
</div>
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