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<h1 class='fqn'><span class='in-band'>Crate <a class="mod" href=''>num</a></span><span class='out-of-band'><span id='render-detail'>
                   <a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">
                       [<span class='inner'>&#x2212;</span>]
                   </a>
               </span><a class='srclink' href='../src/num/lib.rs.html#11-113' title='goto source code'>[src]</a></span></h1>
<div class='docblock'><p>A collection of numeric types and traits for Rust.</p>
<p>This includes new types for big integers, rationals, and complex numbers,
new traits for generic programming on numeric properties like <code>Integer</code>,
and generic range iterators.</p>
<h2 id="example" class="section-header"><a href="#example">Example</a></h2>
<p>This example uses the BigRational type and <a href="https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method">Newton's method</a> to
approximate a square root to arbitrary precision:</p>

<pre class="rust rust-example-rendered">
<span class="kw">extern</span> <span class="kw">crate</span> <span class="ident">num</span>;

<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">FromPrimitive</span>;
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">bigint</span>::<span class="ident">BigInt</span>;
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">rational</span>::{<span class="ident">Ratio</span>, <span class="ident">BigRational</span>};

<span class="kw">fn</span> <span class="ident">approx_sqrt</span>(<span class="ident">number</span>: <span class="ident">u64</span>, <span class="ident">iterations</span>: <span class="ident">usize</span>) <span class="op">-&gt;</span> <span class="ident">BigRational</span> {
    <span class="kw">let</span> <span class="ident">start</span>: <span class="ident">Ratio</span><span class="op">&lt;</span><span class="ident">BigInt</span><span class="op">&gt;</span> <span class="op">=</span> <span class="ident">Ratio</span>::<span class="ident">from_integer</span>(<span class="ident">FromPrimitive</span>::<span class="ident">from_u64</span>(<span class="ident">number</span>).<span class="ident">unwrap</span>());
    <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">approx</span> <span class="op">=</span> <span class="ident">start</span>.<span class="ident">clone</span>();

    <span class="kw">for</span> _ <span class="kw">in</span> <span class="number">0</span>..<span class="ident">iterations</span> {
        <span class="ident">approx</span> <span class="op">=</span> (<span class="kw-2">&amp;</span><span class="ident">approx</span> <span class="op">+</span> (<span class="kw-2">&amp;</span><span class="ident">start</span> <span class="op">/</span> <span class="kw-2">&amp;</span><span class="ident">approx</span>)) <span class="op">/</span>
            <span class="ident">Ratio</span>::<span class="ident">from_integer</span>(<span class="ident">FromPrimitive</span>::<span class="ident">from_u64</span>(<span class="number">2</span>).<span class="ident">unwrap</span>());
    }

    <span class="ident">approx</span>
}

<span class="kw">fn</span> <span class="ident">main</span>() {
    <span class="macro">println</span><span class="macro">!</span>(<span class="string">&quot;{}&quot;</span>, <span class="ident">approx_sqrt</span>(<span class="number">10</span>, <span class="number">4</span>)); <span class="comment">// prints 4057691201/1283082416</span>
}
</pre>
<h2 id="compatibility" class="section-header"><a href="#compatibility">Compatibility</a></h2>
<p>The <code>num</code> crate is tested for rustc 1.8 and greater.</p>
</div><h2 id='modules' class='section-header'><a href="#modules">Modules</a></h2>
<table>
                       <tr class=' module-item'>
                           <td><a class="mod" href="bigint/index.html"
                                  title='mod num::bigint'>bigint</a></td>
                           <td class='docblock-short'>
                                
                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="mod" href="cast/index.html"
                                  title='mod num::cast'>cast</a></td>
                           <td class='docblock-short'>
                                
                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="mod" href="complex/index.html"
                                  title='mod num::complex'>complex</a></td>
                           <td class='docblock-short'>
                                
                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="mod" href="integer/index.html"
                                  title='mod num::integer'>integer</a></td>
                           <td class='docblock-short'>
                                
                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="mod" href="iter/index.html"
                                  title='mod num::iter'>iter</a></td>
                           <td class='docblock-short'>
                                
                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="mod" href="pow/index.html"
                                  title='mod num::pow'>pow</a></td>
                           <td class='docblock-short'>
                                
                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="mod" href="rational/index.html"
                                  title='mod num::rational'>rational</a></td>
                           <td class='docblock-short'>
                                
                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="mod" href="traits/index.html"
                                  title='mod num::traits'>traits</a></td>
                           <td class='docblock-short'>
                                
                           </td>
                       </tr></table><h2 id='structs' class='section-header'><a href="#structs">Structs</a></h2>
<table>
                       <tr class=' module-item'>
                           <td><a class="struct" href="struct.BigInt.html"
                                  title='struct num::BigInt'>BigInt</a></td>
                           <td class='docblock-short'>
                                <p>A big signed integer type.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="struct" href="struct.BigUint.html"
                                  title='struct num::BigUint'>BigUint</a></td>
                           <td class='docblock-short'>
                                <p>A big unsigned integer type.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="struct" href="struct.Complex.html"
                                  title='struct num::Complex'>Complex</a></td>
                           <td class='docblock-short'>
                                <p>A complex number in Cartesian form.</p>

                           </td>
                       </tr></table><h2 id='traits' class='section-header'><a href="#traits">Traits</a></h2>
<table>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.Bounded.html"
                                  title='trait num::Bounded'>Bounded</a></td>
                           <td class='docblock-short'>
                                <p>Numbers which have upper and lower bounds</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.CheckedAdd.html"
                                  title='trait num::CheckedAdd'>CheckedAdd</a></td>
                           <td class='docblock-short'>
                                <p>Performs addition that returns <code>None</code> instead of wrapping around on
overflow.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.CheckedDiv.html"
                                  title='trait num::CheckedDiv'>CheckedDiv</a></td>
                           <td class='docblock-short'>
                                <p>Performs division that returns <code>None</code> instead of panicking on division by zero and instead of
wrapping around on underflow and overflow.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.CheckedMul.html"
                                  title='trait num::CheckedMul'>CheckedMul</a></td>
                           <td class='docblock-short'>
                                <p>Performs multiplication that returns <code>None</code> instead of wrapping around on underflow or
overflow.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.CheckedSub.html"
                                  title='trait num::CheckedSub'>CheckedSub</a></td>
                           <td class='docblock-short'>
                                <p>Performs subtraction that returns <code>None</code> instead of wrapping around on underflow.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.Float.html"
                                  title='trait num::Float'>Float</a></td>
                           <td class='docblock-short'>
                                <p>Generic trait for floating point numbers</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.FromPrimitive.html"
                                  title='trait num::FromPrimitive'>FromPrimitive</a></td>
                           <td class='docblock-short'>
                                <p>A generic trait for converting a number to a value.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.Integer.html"
                                  title='trait num::Integer'>Integer</a></td>
                           <td class='docblock-short'>
                                
                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.Num.html"
                                  title='trait num::Num'>Num</a></td>
                           <td class='docblock-short'>
                                <p>The base trait for numeric types, covering <code>0</code> and <code>1</code> values,
comparisons, basic numeric operations, and string conversion.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.NumCast.html"
                                  title='trait num::NumCast'>NumCast</a></td>
                           <td class='docblock-short'>
                                <p>An interface for casting between machine scalars.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.One.html"
                                  title='trait num::One'>One</a></td>
                           <td class='docblock-short'>
                                <p>Defines a multiplicative identity element for <code>Self</code>.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.PrimInt.html"
                                  title='trait num::PrimInt'>PrimInt</a></td>
                           <td class='docblock-short'>
                                
                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.Saturating.html"
                                  title='trait num::Saturating'>Saturating</a></td>
                           <td class='docblock-short'>
                                <p>Saturating math operations</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.Signed.html"
                                  title='trait num::Signed'>Signed</a></td>
                           <td class='docblock-short'>
                                <p>Useful functions for signed numbers (i.e. numbers that can be negative).</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.ToPrimitive.html"
                                  title='trait num::ToPrimitive'>ToPrimitive</a></td>
                           <td class='docblock-short'>
                                <p>A generic trait for converting a value to a number.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.Unsigned.html"
                                  title='trait num::Unsigned'>Unsigned</a></td>
                           <td class='docblock-short'>
                                <p>A trait for values which cannot be negative</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="trait" href="trait.Zero.html"
                                  title='trait num::Zero'>Zero</a></td>
                           <td class='docblock-short'>
                                <p>Defines an additive identity element for <code>Self</code>.</p>

                           </td>
                       </tr></table><h2 id='functions' class='section-header'><a href="#functions">Functions</a></h2>
<table>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.abs.html"
                                  title='fn num::abs'>abs</a></td>
                           <td class='docblock-short'>
                                <p>Computes the absolute value.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.abs_sub.html"
                                  title='fn num::abs_sub'>abs_sub</a></td>
                           <td class='docblock-short'>
                                <p>The positive difference of two numbers.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.checked_pow.html"
                                  title='fn num::checked_pow'>checked_pow</a></td>
                           <td class='docblock-short'>
                                <p>Raises a value to the power of exp, returning <code>None</code> if an overflow occurred.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.clamp.html"
                                  title='fn num::clamp'>clamp</a></td>
                           <td class='docblock-short'>
                                <p>A value bounded by a minimum and a maximum</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.one.html"
                                  title='fn num::one'>one</a></td>
                           <td class='docblock-short'>
                                <p>Returns the multiplicative identity, <code>1</code>.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.range.html"
                                  title='fn num::range'>range</a></td>
                           <td class='docblock-short'>
                                <p>Returns an iterator over the given range [start, stop) (that is, starting
at start (inclusive), and ending at stop (exclusive)).</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.range_inclusive.html"
                                  title='fn num::range_inclusive'>range_inclusive</a></td>
                           <td class='docblock-short'>
                                <p>Return an iterator over the range [start, stop]</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.range_step.html"
                                  title='fn num::range_step'>range_step</a></td>
                           <td class='docblock-short'>
                                <p>Return an iterator over the range [start, stop) by <code>step</code>. It handles overflow by stopping.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.range_step_inclusive.html"
                                  title='fn num::range_step_inclusive'>range_step_inclusive</a></td>
                           <td class='docblock-short'>
                                <p>Return an iterator over the range [start, stop] by <code>step</code>. It handles overflow by stopping.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.signum.html"
                                  title='fn num::signum'>signum</a></td>
                           <td class='docblock-short'>
                                <p>Returns the sign of the number.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="fn" href="fn.zero.html"
                                  title='fn num::zero'>zero</a></td>
                           <td class='docblock-short'>
                                <p>Returns the additive identity, <code>0</code>.</p>

                           </td>
                       </tr></table><h2 id='types' class='section-header'><a href="#types">Type Definitions</a></h2>
<table>
                       <tr class=' module-item'>
                           <td><a class="type" href="type.BigRational.html"
                                  title='type num::BigRational'>BigRational</a></td>
                           <td class='docblock-short'>
                                <p>Alias for arbitrary precision rationals.</p>

                           </td>
                       </tr>
                       <tr class=' module-item'>
                           <td><a class="type" href="type.Rational.html"
                                  title='type num::Rational'>Rational</a></td>
                           <td class='docblock-short'>
                                <p>Alias for a <code>Ratio</code> of machine-sized integers.</p>

                           </td>
                       </tr></table></section>
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