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<!DOCTYPE html>
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<h1 class='fqn'><span class='in-band'>Crate <a class='mod' href=''>complex</a></span><span class='out-of-band'><span id='render-detail'>
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<div class='docblock'><p><a href="https://en.wikipedia.org/wiki/Complex_number">Complex numbers</a>.</p>
</div><h2 id='structs' class='section-header'><a href="#structs">Structs</a></h2>
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<td><a class='struct' href='struct.c32.html'
title='complex::c32'>c32</a></td>
<td class='docblock short'>
<p>A complex number with 32-bit parts.</p>
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<td><a class='struct' href='struct.c64.html'
title='complex::c64'>c64</a></td>
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<p>A complex number with 64-bit parts.</p>
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<td><a class='trait' href='trait.Complex.html'
title='complex::Complex'>Complex</a></td>
<td class='docblock short'>
<p>A complex number.</p>
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<td><a class='trait' href='trait.Number.html'
title='complex::Number'>Number</a></td>
<td class='docblock short'>
<p>A number.</p>
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<td><a class='trait' href='trait.Real.html'
title='complex::Real'>Real</a></td>
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<p>A real number.</p>
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<!DOCTYPE html>
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<section id='main' class="content struct">
<h1 class='fqn'><span class='in-band'>Struct <a href='index.html'>complex</a>::<wbr><a class='struct' href=''>c32</a></span><span class='out-of-band'><span id='render-detail'>
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<pre class='rust struct'>pub struct c32(pub <a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a>, pub <a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a>);</pre><div class='docblock'><p>A complex number with 32-bit parts.</p>
</div><h2 id='implementations'>Trait Implementations</h2><h3 class='impl'><code>impl <a class='trait' href='../complex/trait.Number.html' title='complex::Number'>Number</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'></div><h3 class='impl'><code>impl <a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Complex</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='assoc_type.Real' class='type'><code>type Real = <a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a></code></h4>
<h4 id='method.new' class='method'><code>fn <a href='../complex/trait.Complex.html#method.new' class='fnname'>new</a>(re: Self::Real, im: Self::Real) -&gt; <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h4>
<h4 id='method.from_polar' class='method'><code>fn <a href='../complex/trait.Complex.html#method.from_polar' class='fnname'>from_polar</a>(abs: Self::Real, arg: Self::Real) -&gt; Self</code></h4>
<h4 id='method.re' class='method'><code>fn <a href='../complex/trait.Complex.html#method.re' class='fnname'>re</a>(&amp;self) -&gt; Self::Real</code></h4>
<h4 id='method.re_mut' class='method'><code>fn <a href='../complex/trait.Complex.html#method.re_mut' class='fnname'>re_mut</a>(&amp;mut self) -&gt; &amp;mut Self::Real</code></h4>
<h4 id='method.im' class='method'><code>fn <a href='../complex/trait.Complex.html#method.im' class='fnname'>im</a>(&amp;self) -&gt; Self::Real</code></h4>
<h4 id='method.im_mut' class='method'><code>fn <a href='../complex/trait.Complex.html#method.im_mut' class='fnname'>im_mut</a>(&amp;mut self) -&gt; &amp;mut Self::Real</code></h4>
<h4 id='method.abs' class='method'><code>fn <a href='../complex/trait.Complex.html#method.abs' class='fnname'>abs</a>(&amp;self) -&gt; Self::Real</code></h4>
<h4 id='method.arg' class='method'><code>fn <a href='../complex/trait.Complex.html#method.arg' class='fnname'>arg</a>(&amp;self) -&gt; Self::Real</code></h4>
<h4 id='method.to_polar' class='method'><code>fn <a href='../complex/trait.Complex.html#method.to_polar' class='fnname'>to_polar</a>(&amp;self) -&gt; <a href='http://doc.rust-lang.org/nightly/std/primitive.tuple.html'>(Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>, Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>)</a></code></h4>
<h4 id='method.conj' class='method'><code>fn <a href='../complex/trait.Complex.html#method.conj' class='fnname'>conj</a>(&amp;self) -&gt; Self</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Add.html' title='core::ops::Add'>Add</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.add' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Add.html#method.add' class='fnname'>add</a>(self, rhs: Self) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Add.html' title='core::ops::Add'>Add</a>&lt;<a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a>&gt; for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.add' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Add.html#method.add' class='fnname'>add</a>(self, rhs: <a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a>) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Div.html' title='core::ops::Div'>Div</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.div' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Div.html#method.div' class='fnname'>div</a>(self, rhs: Self) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Div.html' title='core::ops::Div'>Div</a>&lt;<a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a>&gt; for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.div' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Div.html#method.div' class='fnname'>div</a>(self, rhs: <a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a>) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Mul.html' title='core::ops::Mul'>Mul</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.mul' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Mul.html#method.mul' class='fnname'>mul</a>(self, rhs: Self) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Mul.html' title='core::ops::Mul'>Mul</a>&lt;<a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a>&gt; for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.mul' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Mul.html#method.mul' class='fnname'>mul</a>(self, rhs: <a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a>) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Neg.html' title='core::ops::Neg'>Neg</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.neg' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Neg.html#method.neg' class='fnname'>neg</a>(self) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Sub.html' title='core::ops::Sub'>Sub</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.sub' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Sub.html#method.sub' class='fnname'>sub</a>(self, rhs: Self) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Sub.html' title='core::ops::Sub'>Sub</a>&lt;<a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a>&gt; for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.sub' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Sub.html#method.sub' class='fnname'>sub</a>(self, rhs: <a href='http://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a>) -&gt; Self::Output</code></h4>
</div><h3 id='derived_implementations'>Derived Implementations </h3><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html' title='core::cmp::PartialEq'>PartialEq</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='method.eq' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html#method.eq' class='fnname'>eq</a>(&amp;self, __arg_0: &amp;<a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a>) -&gt; <a href='http://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a></code></h4>
<h4 id='method.ne' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html#method.ne' class='fnname'>ne</a>(&amp;self, __arg_0: &amp;<a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a>) -&gt; <a href='http://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a></code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html' title='core::fmt::Debug'>Debug</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='method.fmt' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html#method.fmt' class='fnname'>fmt</a>(&amp;self, __arg_0: &amp;mut <a class='struct' href='http://doc.rust-lang.org/nightly/core/fmt/struct.Formatter.html' title='core::fmt::Formatter'>Formatter</a>) -&gt; <a class='type' href='http://doc.rust-lang.org/nightly/core/fmt/type.Result.html' title='core::fmt::Result'>Result</a></code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/marker/trait.Copy.html' title='core::marker::Copy'>Copy</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'></div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/clone/trait.Clone.html' title='core::clone::Clone'>Clone</a> for <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h3><div class='impl-items'><h4 id='method.clone' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/clone/trait.Clone.html#method.clone' class='fnname'>clone</a>(&amp;self) -&gt; <a class='struct' href='../complex/struct.c32.html' title='complex::c32'>c32</a></code></h4>
<h4 id='method.clone_from' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/clone/trait.Clone.html#method.clone_from' class='fnname'>clone_from</a>(&amp;mut self, source: &amp;Self)</code></h4>
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<h1 class='fqn'><span class='in-band'>Struct <a href='index.html'>complex</a>::<wbr><a class='struct' href=''>c64</a></span><span class='out-of-band'><span id='render-detail'>
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<pre class='rust struct'>pub struct c64(pub <a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a>, pub <a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a>);</pre><div class='docblock'><p>A complex number with 64-bit parts.</p>
</div><h2 id='implementations'>Trait Implementations</h2><h3 class='impl'><code>impl <a class='trait' href='../complex/trait.Number.html' title='complex::Number'>Number</a> for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'></div><h3 class='impl'><code>impl <a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Complex</a> for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='assoc_type.Real' class='type'><code>type Real = <a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a></code></h4>
<h4 id='method.new' class='method'><code>fn <a href='../complex/trait.Complex.html#method.new' class='fnname'>new</a>(re: Self::Real, im: Self::Real) -&gt; <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h4>
<h4 id='method.from_polar' class='method'><code>fn <a href='../complex/trait.Complex.html#method.from_polar' class='fnname'>from_polar</a>(abs: Self::Real, arg: Self::Real) -&gt; Self</code></h4>
<h4 id='method.re' class='method'><code>fn <a href='../complex/trait.Complex.html#method.re' class='fnname'>re</a>(&amp;self) -&gt; Self::Real</code></h4>
<h4 id='method.re_mut' class='method'><code>fn <a href='../complex/trait.Complex.html#method.re_mut' class='fnname'>re_mut</a>(&amp;mut self) -&gt; &amp;mut Self::Real</code></h4>
<h4 id='method.im' class='method'><code>fn <a href='../complex/trait.Complex.html#method.im' class='fnname'>im</a>(&amp;self) -&gt; Self::Real</code></h4>
<h4 id='method.im_mut' class='method'><code>fn <a href='../complex/trait.Complex.html#method.im_mut' class='fnname'>im_mut</a>(&amp;mut self) -&gt; &amp;mut Self::Real</code></h4>
<h4 id='method.abs' class='method'><code>fn <a href='../complex/trait.Complex.html#method.abs' class='fnname'>abs</a>(&amp;self) -&gt; Self::Real</code></h4>
<h4 id='method.arg' class='method'><code>fn <a href='../complex/trait.Complex.html#method.arg' class='fnname'>arg</a>(&amp;self) -&gt; Self::Real</code></h4>
<h4 id='method.to_polar' class='method'><code>fn <a href='../complex/trait.Complex.html#method.to_polar' class='fnname'>to_polar</a>(&amp;self) -&gt; <a href='http://doc.rust-lang.org/nightly/std/primitive.tuple.html'>(Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>, Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>)</a></code></h4>
<h4 id='method.conj' class='method'><code>fn <a href='../complex/trait.Complex.html#method.conj' class='fnname'>conj</a>(&amp;self) -&gt; Self</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Add.html' title='core::ops::Add'>Add</a> for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.add' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Add.html#method.add' class='fnname'>add</a>(self, rhs: Self) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Add.html' title='core::ops::Add'>Add</a>&lt;<a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a>&gt; for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.add' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Add.html#method.add' class='fnname'>add</a>(self, rhs: <a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a>) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Div.html' title='core::ops::Div'>Div</a> for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.div' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Div.html#method.div' class='fnname'>div</a>(self, rhs: Self) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Div.html' title='core::ops::Div'>Div</a>&lt;<a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a>&gt; for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.div' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Div.html#method.div' class='fnname'>div</a>(self, rhs: <a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a>) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Mul.html' title='core::ops::Mul'>Mul</a> for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.mul' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Mul.html#method.mul' class='fnname'>mul</a>(self, rhs: Self) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Mul.html' title='core::ops::Mul'>Mul</a>&lt;<a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a>&gt; for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.mul' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Mul.html#method.mul' class='fnname'>mul</a>(self, rhs: <a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a>) -&gt; Self::Output</code></h4>
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<h4 id='method.neg' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Neg.html#method.neg' class='fnname'>neg</a>(self) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Sub.html' title='core::ops::Sub'>Sub</a> for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.sub' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Sub.html#method.sub' class='fnname'>sub</a>(self, rhs: Self) -&gt; Self::Output</code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Sub.html' title='core::ops::Sub'>Sub</a>&lt;<a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a>&gt; for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='assoc_type.Output' class='type'><code>type Output = Self</code></h4>
<h4 id='method.sub' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/ops/trait.Sub.html#method.sub' class='fnname'>sub</a>(self, rhs: <a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a>) -&gt; Self::Output</code></h4>
</div><h3 id='derived_implementations'>Derived Implementations </h3><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html' title='core::cmp::PartialEq'>PartialEq</a> for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='method.eq' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html#method.eq' class='fnname'>eq</a>(&amp;self, __arg_0: &amp;<a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a>) -&gt; <a href='http://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a></code></h4>
<h4 id='method.ne' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html#method.ne' class='fnname'>ne</a>(&amp;self, __arg_0: &amp;<a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a>) -&gt; <a href='http://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a></code></h4>
</div><h3 class='impl'><code>impl <a class='trait' href='http://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html' title='core::fmt::Debug'>Debug</a> for <a class='struct' href='../complex/struct.c64.html' title='complex::c64'>c64</a></code></h3><div class='impl-items'><h4 id='method.fmt' class='method'><code>fn <a href='http://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html#method.fmt' class='fnname'>fmt</a>(&amp;self, __arg_0: &amp;mut <a class='struct' href='http://doc.rust-lang.org/nightly/core/fmt/struct.Formatter.html' title='core::fmt::Formatter'>Formatter</a>) -&gt; <a class='type' href='http://doc.rust-lang.org/nightly/core/fmt/type.Result.html' title='core::fmt::Result'>Result</a></code></h4>
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<h1 class='fqn'><span class='in-band'>Trait <a href='index.html'>complex</a>::<wbr><a class='trait' href=''>Complex</a></span><span class='out-of-band'><span id='render-detail'>
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<pre class='rust trait'>pub trait Complex: <a class='trait' href='../complex/trait.Number.html' title='complex::Number'>Number</a> {
type Real: <a class='trait' href='../complex/trait.Real.html' title='complex::Real'>Real</a>;
fn <a href='#tymethod.new' class='fnname'>new</a>(Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>, Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>) -&gt; Self;
fn <a href='#tymethod.from_polar' class='fnname'>from_polar</a>(Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>, Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>) -&gt; Self;
fn <a href='#tymethod.re' class='fnname'>re</a>(&amp;self) -&gt; Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>;
fn <a href='#tymethod.re_mut' class='fnname'>re_mut</a>(&amp;mut self) -&gt; &amp;mut Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>;
fn <a href='#tymethod.im' class='fnname'>im</a>(&amp;self) -&gt; Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>;
fn <a href='#tymethod.im_mut' class='fnname'>im_mut</a>(&amp;mut self) -&gt; &amp;mut Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>;
fn <a href='#tymethod.abs' class='fnname'>abs</a>(&amp;self) -&gt; Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>;
fn <a href='#tymethod.arg' class='fnname'>arg</a>(&amp;self) -&gt; Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>;
fn <a href='#method.to_polar' class='fnname'>to_polar</a>(&amp;self) -&gt; <a href='http://doc.rust-lang.org/nightly/std/primitive.tuple.html'>(Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>, Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>)</a> { ... }
fn <a href='#method.conj' class='fnname'>conj</a>(&amp;self) -&gt; Self { ... }
}</pre><div class='docblock'><p>A complex number.</p>
</div>
<h2 id='associated-types'>Associated Types</h2>
<div class='methods'>
<h3 id='associatedtype.Real' class='method stab '><code>type Real: <a class='trait' href='../complex/trait.Real.html' title='complex::Real'>Real</a></code></h3><div class='docblock'><p>A real number.</p>
</div></div>
<h2 id='required-methods'>Required Methods</h2>
<div class='methods'>
<h3 id='tymethod.new' class='method stab '><code>fn <a href='#tymethod.new' class='fnname'>new</a>(Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>, Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>) -&gt; Self</code></h3><div class='docblock'><p>Create a complex number from a real and an imaginary part.</p>
</div><h3 id='tymethod.from_polar' class='method stab '><code>fn <a href='#tymethod.from_polar' class='fnname'>from_polar</a>(Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>, Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a>) -&gt; Self</code></h3><div class='docblock'><p>Create a complex number from a modulus and an argument.</p>
</div><h3 id='tymethod.re' class='method stab '><code>fn <a href='#tymethod.re' class='fnname'>re</a>(&amp;self) -&gt; Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a></code></h3><div class='docblock'><p>Return the real part.</p>
</div><h3 id='tymethod.re_mut' class='method stab '><code>fn <a href='#tymethod.re_mut' class='fnname'>re_mut</a>(&amp;mut self) -&gt; &amp;mut Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a></code></h3><div class='docblock'><p>Return the real part as a mutable reference.</p>
</div><h3 id='tymethod.im' class='method stab '><code>fn <a href='#tymethod.im' class='fnname'>im</a>(&amp;self) -&gt; Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a></code></h3><div class='docblock'><p>Return the imaginary part.</p>
</div><h3 id='tymethod.im_mut' class='method stab '><code>fn <a href='#tymethod.im_mut' class='fnname'>im_mut</a>(&amp;mut self) -&gt; &amp;mut Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a></code></h3><div class='docblock'><p>Return the imaginary part as a mutable reference.</p>
</div><h3 id='tymethod.abs' class='method stab '><code>fn <a href='#tymethod.abs' class='fnname'>abs</a>(&amp;self) -&gt; Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a></code></h3><div class='docblock'><p>Compute the modulus.</p>
</div><h3 id='tymethod.arg' class='method stab '><code>fn <a href='#tymethod.arg' class='fnname'>arg</a>(&amp;self) -&gt; Self::<a class='trait' href='../complex/trait.Complex.html' title='complex::Complex'>Real</a></code></h3><div class='docblock'><p>Compute the argument.</p>
</div></div>
<h2 id='provided-methods'>Provided Methods</h2>
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<pre class='rust trait'>pub trait Number: <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Add.html' title='core::ops::Add'>Add</a>&lt;Output=Self&gt; + <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Div.html' title='core::ops::Div'>Div</a>&lt;Output=Self&gt; + <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Mul.html' title='core::ops::Mul'>Mul</a>&lt;Output=Self&gt; + <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Neg.html' title='core::ops::Neg'>Neg</a>&lt;Output=Self&gt; + <a class='trait' href='http://doc.rust-lang.org/nightly/core/ops/trait.Sub.html' title='core::ops::Sub'>Sub</a>&lt;Output=Self&gt; + <a class='trait' href='http://doc.rust-lang.org/nightly/core/marker/trait.Copy.html' title='core::marker::Copy'>Copy</a> + <a class='trait' href='http://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html' title='core::fmt::Debug'>Debug</a> + <a class='trait' href='http://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html' title='core::cmp::PartialEq'>PartialEq</a> { }</pre><div class='docblock'><p>A number.</p>
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<pre class='rust trait'>pub trait Real: <a class='trait' href='../complex/trait.Number.html' title='complex::Number'>Number</a> { }</pre><div class='docblock'><p>A real number.</p>
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<pre class='rust fn'>pub fn backward(data: <a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>&amp;mut [</a><a class='struct' href='../../complex/struct.c64.html' title='complex::c64'>c64</a><a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>]</a>)</pre><div class='docblock'><p>Perform the backward transform.</p>
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<pre class='rust fn'>pub fn forward(data: <a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>&amp;mut [</a><a class='struct' href='../../complex/struct.c64.html' title='complex::c64'>c64</a><a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>]</a>)</pre><div class='docblock'><p>Perform the forward transform.</p>
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<pre class='rust fn'>pub fn inverse(data: <a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>&amp;mut [</a><a class='struct' href='../../complex/struct.c64.html' title='complex::c64'>c64</a><a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>]</a>)</pre><div class='docblock'><p>Perform the inverse transform.</p>
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<pre class='rust fn'>pub fn backward(data: <a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>&amp;mut [</a><a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a><a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>]</a>)</pre><div class='docblock'><p>Perform the backward transform.</p>
<p>The number of points should be a power of two. The data should be packed as
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<pre class='rust fn'>pub fn forward(data: <a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>&amp;mut [</a><a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a><a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>]</a>)</pre><div class='docblock'><p>Perform the forward transform.</p>
<p>The number of points should be a power of two. The data are replaced by the
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<li>William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P.
Flannery, “Numerical Recipes 3rd Edition: The Art of Scientific
Computing,” Cambridge University Press, 2007.</li>
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<pre class='rust fn'>pub fn inverse(data: <a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>&amp;mut [</a><a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a><a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>]</a>)</pre><div class='docblock'><p>Perform the inverse transform.</p>
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<pre class='rust fn'>pub fn unpack(data: <a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>&amp;[</a><a href='http://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a><a href='http://doc.rust-lang.org/nightly/std/primitive.slice.html'>]</a>) -&gt; <a class='struct' href='http://doc.rust-lang.org/nightly/collections/vec/struct.Vec.html' title='collections::vec::Vec'>Vec</a>&lt;<a class='struct' href='../../complex/struct.c64.html' title='complex::c64'>c64</a>&gt;</pre><div class='docblock'><p>Unpack a compressed representation produced by <code>real::forward</code>.</p>
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<div class='docblock'><p>Transformation of real data.</p>
</div><h2 id='functions' class='section-header'><a href="#functions">Functions</a></h2>
<table>
<tr class=' module-item'>
<td><a class='fn' href='fn.backward.html'
title='dft::real::backward'>backward</a></td>
<td class='docblock short'>
<p>Perform the backward transform.</p>
</td>
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<td><a class='fn' href='fn.forward.html'
title='dft::real::forward'>forward</a></td>
<td class='docblock short'>
<p>Perform the forward transform.</p>
</td>
</tr>
<tr class=' module-item'>
<td><a class='fn' href='fn.inverse.html'
title='dft::real::inverse'>inverse</a></td>
<td class='docblock short'>
<p>Perform the inverse transform.</p>
</td>
</tr>
<tr class=' module-item'>
<td><a class='fn' href='fn.unpack.html'
title='dft::real::unpack'>unpack</a></td>
<td class='docblock short'>
<p>Unpack a compressed representation produced by <code>real::forward</code>.</p>
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implementors/complex/trait.Complex.js
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implementors/complex/trait.Number.js
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/**
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*
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.docblock h1 { font-size: 1.3em; }
.docblock h2 { font-size: 1.15em; }
.docblock h3, .docblock h4, .docblock h5 { font-size: 1em; }
.content .out-of-band {
font-size: 23px;
width: 40%;
margin: 0px;
padding: 0px;
text-align: right;
display: inline-block;
}
.content .in-band {
width: 60%;
margin: 0px;
padding: 0px;
display: inline-block;
}
.content table {
border-spacing: 0 5px;
border-collapse: separate;
}
.content td { vertical-align: top; }
.content td:first-child { padding-right: 20px; }
.content td p:first-child { margin-top: 0; }
.content td h1, .content td h2 { margin-left: 0; font-size: 1.1em; }
.docblock table {
border: 1px solid #ddd;
margin: .5em 0;
border-collapse: collapse;
width: 100%;
}
.docblock table td {
padding: .5em;
border-top: 1px dashed #ddd;
border-bottom: 1px dashed #ddd;
}
.docblock table th {
padding: .5em;
text-align: left;
border-top: 1px solid #ddd;
border-bottom: 1px solid #ddd;
}
.content .item-list {
list-style-type: none;
padding: 0;
}
.content .item-list li { margin-bottom: 3px; }
.content .multi-column {
-moz-column-count: 5;
-moz-column-gap: 2.5em;
-webkit-column-count: 5;
-webkit-column-gap: 2.5em;
column-count: 5;
column-gap: 2.5em;
}
.content .multi-column li { width: 100%; display: inline-block; }
.content .method {
font-size: 1em;
position: relative;
}
/* Shift "where ..." part of method definition down a line */
.content .method .where { display: block; }
/* Bit of whitespace to indent it */
.content .method .where::before { content: ' '; }
.content .methods > div { margin-left: 40px; }
.content .impl-items .docblock, .content .impl-items .stability {
margin-left: 40px;
}
.content .impl-items .method, .content .impl-items .type {
margin-left: 20px;
}
nav {
border-bottom: 1px solid #e0e0e0;
padding-bottom: 10px;
margin-bottom: 10px;
}
nav.main {
padding: 20px 0;
text-align: center;
}
nav.main .current {
border-top: 1px solid #000;
border-bottom: 1px solid #000;
}
nav.main .separator {
border: 1px solid #000;
display: inline-block;
height: 23px;
margin: 0 20px;
}
nav.sum { text-align: right; }
nav.sub form { display: inline; }
nav, .content {
margin-left: 230px;
}
a {
text-decoration: none;
color: #000;
background: transparent;
}
.docblock a {
color: #4e8bca;
}
.docblock a:hover {
text-decoration: underline;
}
.content span.trait, .content a.trait, .block a.current.trait { color: #8866ff; }
.content span.mod, .content a.mod, block a.current.mod { color: #4d76ae; }
.content span.enum, .content a.enum, .block a.current.enum { color: #5e9766; }
.content span.struct, .content a.struct, .block a.current.struct { color: #e53700; }
.content span.fn, .content a.fn, .block a.current.fn { color: #8c6067; }
.content span.method, .content a.method, .block a.current.method { color: #8c6067; }
.content span.tymethod, .content a.tymethod, .block a.current.tymethod { color: #8c6067; }
.content .fnname { color: #8c6067; }
.search-input {
width: 100%;
/* Override Normalize.css: we have margins and do
not want to overflow - the `moz` attribute is necessary
until Firefox 29, too early to drop at this point */
-moz-box-sizing: border-box !important;
box-sizing: border-box !important;
outline: none;
border: none;
border-radius: 1px;
color: #555;
margin-top: 5px;
padding: 10px 16px;
font-size: 17px;
box-shadow: 0 0 0 1px #e0e0e0, 0 0 0 2px transparent;
transition: border-color 300ms ease;
transition: border-radius 300ms ease-in-out;
transition: box-shadow 300ms ease-in-out;
}
.search-input:focus {
border-color: #66afe9;
border-radius: 2px;
border: 0;
outline: 0;
box-shadow: 0 0 8px #078dd8;
}
.search-results .desc {
white-space: nowrap;
text-overflow: ellipsis;
overflow: hidden;
display: block;
}
.search-results a {
display: block;
}
.content .search-results td:first-child { padding-right: 0; }
.content .search-results td:first-child a { padding-right: 10px; }
#help {
background: #e9e9e9;
border-radius: 4px;
box-shadow: 0 0 6px rgba(0,0,0,.2);
position: absolute;
top: 300px;
left: 50%;
margin-top: -125px;
margin-left: -275px;
width: 550px;
height: 300px;
border: 1px solid #bfbfbf;
}
#help dt {
float: left;
border-radius: 3px;
border: 1px solid #bfbfbf;
background: #fff;
width: 23px;
text-align: center;
clear: left;
display: block;
margin-top: -1px;
}
#help dd { margin: 5px 33px; }
#help .infos { padding-left: 0; }
#help h1 { margin-top: 0; }
#help div {
width: 50%;
float: left;
padding: 20px;
}
em.stab.unstable { background: #FFF5D6; border-color: #FFC600; }
em.stab.deprecated { background: #F3DFFF; border-color: #7F0087; }
em.stab {
display: inline-block;
border-width: 1px;
border-style: solid;
padding: 3px;
margin-bottom: 5px;
font-size: 90%;
font-style: normal;
}
em.stab p {
display: inline;
}
.module-item .stab {
border-width: 0;
padding: 0;
margin: 0;
background: inherit !important;
}
.module-item.unstable {
opacity: 0.65;
}
td.summary-column {
width: 100%;
}
.summary {
padding-right: 0px;
}
:target { background: #FDFFD3; }
.line-numbers :target { background-color: transparent; }
/* Code highlighting */
pre.rust .kw { color: #8959A8; }
pre.rust .kw-2, pre.rust .prelude-ty { color: #4271AE; }
pre.rust .number, pre.rust .string { color: #718C00; }
pre.rust .self, pre.rust .boolval, pre.rust .prelude-val,
pre.rust .attribute, pre.rust .attribute .ident { color: #C82829; }
pre.rust .comment { color: #8E908C; }
pre.rust .doccomment { color: #4D4D4C; }
pre.rust .macro, pre.rust .macro-nonterminal { color: #3E999F; }
pre.rust .lifetime { color: #B76514; }
.rusttest { display: none; }
pre.rust { position: relative; }
.test-arrow {
display: inline-block;
position: absolute;
top: 0;
right: 10px;
font-size: 150%;
-webkit-transform: scaleX(-1);
transform: scaleX(-1);
}
.methods .section-header {
/* Override parent class attributes. */
border-bottom: none !important;
font-size: 1.1em !important;
margin: 0 0 -5px;
padding: 0;
}
.section-header:hover a:after {
content: '\2002\00a7\2002';
}
.section-header:hover a {
text-decoration: none;
}
.section-header a {
color: inherit;
}
.collapse-toggle {
font-weight: 300;
position: absolute;
left: -23px;
color: #999;
top: 0;
}
.toggle-wrapper > .collapse-toggle {
left: -24px;
margin-top: 0px;
}
.toggle-wrapper {
position: relative;
}
.toggle-wrapper.collapsed {
height: 1em;
transition: height .2s;
}
.collapse-toggle > .inner {
display: inline-block;
width: 1.2ch;
text-align: center;
}
.toggle-label {
color: #999;
}
/* Media Queries */
@media (max-width: 700px) {
body {
padding-top: 0px;
}
.sidebar {
height: 40px;
min-height: 40px;
width: 100%;
margin: 0px;
padding: 0px;
position: static;
}
.sidebar .location {
float: left;
margin: 0px;
padding: 5px;
width: 60%;
background: inherit;
text-align: left;
font-size: 24px;
}
.sidebar img {
width: 35px;
margin-top: 5px;
margin-bottom: 0px;
float: left;
}
nav.sub {
margin: 0 auto;
}
.sidebar .block {
display: none;
}
.content {
margin-left: 0px;
}
.content .in-band {
width: 100%;
}
.content .out-of-band {
display: none;
}
.toggle-wrapper > .collapse-toggle {
left: 0px;
}
.toggle-wrapper {
height: 1.5em;
}
}
@media print {
nav.sub, .content .out-of-band, .collapse-toggle {
display: none;
}
}

915
main.js
View File

@ -0,0 +1,915 @@
// Copyright 2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
/*jslint browser: true, es5: true */
/*globals $: true, rootPath: true */
(function() {
"use strict";
var resizeTimeout, interval;
// This mapping table should match the discriminants of
// `rustdoc::html::item_type::ItemType` type in Rust.
var itemTypes = ["mod",
"externcrate",
"import",
"struct",
"enum",
"fn",
"type",
"static",
"trait",
"impl",
"tymethod",
"method",
"structfield",
"variant",
"macro",
"primitive",
"associatedtype",
"constant",
"associatedconstant"];
$('.js-only').removeClass('js-only');
function getQueryStringParams() {
var params = {};
window.location.search.substring(1).split("&").
map(function(s) {
var pair = s.split("=");
params[decodeURIComponent(pair[0])] =
typeof pair[1] === "undefined" ?
null : decodeURIComponent(pair[1]);
});
return params;
}
function browserSupportsHistoryApi() {
return window.history && typeof window.history.pushState === "function";
}
function highlightSourceLines(ev) {
var i, from, to, match = window.location.hash.match(/^#?(\d+)(?:-(\d+))?$/);
if (match) {
from = parseInt(match[1], 10);
to = Math.min(50000, parseInt(match[2] || match[1], 10));
from = Math.min(from, to);
if ($('#' + from).length === 0) {
return;
}
if (ev === null) $('#' + from)[0].scrollIntoView();
$('.line-numbers span').removeClass('line-highlighted');
for (i = from; i <= to; ++i) {
$('#' + i).addClass('line-highlighted');
}
}
}
highlightSourceLines(null);
$(window).on('hashchange', highlightSourceLines);
$(document).on('keyup', function(e) {
if (document.activeElement.tagName === 'INPUT') {
return;
}
if (e.which === 191) { // question mark
if (e.shiftKey && $('#help').hasClass('hidden')) {
e.preventDefault();
$('#help').removeClass('hidden');
}
} else if (e.which === 27) { // esc
if (!$('#help').hasClass('hidden')) {
e.preventDefault();
$('#help').addClass('hidden');
} else if (!$('#search').hasClass('hidden')) {
e.preventDefault();
$('#search').addClass('hidden');
$('#main').removeClass('hidden');
}
} else if (e.which === 83) { // S
e.preventDefault();
$('.search-input').focus();
}
}).on('click', function(e) {
if (!$(e.target).closest('#help').length) {
$('#help').addClass('hidden');
}
});
$('.version-selector').on('change', function() {
var i, match,
url = document.location.href,
stripped = '',
len = rootPath.match(/\.\.\//g).length + 1;
for (i = 0; i < len; ++i) {
match = url.match(/\/[^\/]*$/);
if (i < len - 1) {
stripped = match[0] + stripped;
}
url = url.substring(0, url.length - match[0].length);
}
url += '/' + $('.version-selector').val() + stripped;
document.location.href = url;
});
/**
* A function to compute the Levenshtein distance between two strings
* Licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported
* Full License can be found at http://creativecommons.org/licenses/by-sa/3.0/legalcode
* This code is an unmodified version of the code written by Marco de Wit
* and was found at http://stackoverflow.com/a/18514751/745719
*/
var levenshtein = (function() {
var row2 = [];
return function(s1, s2) {
if (s1 === s2) {
return 0;
} else {
var s1_len = s1.length, s2_len = s2.length;
if (s1_len && s2_len) {
var i1 = 0, i2 = 0, a, b, c, c2, row = row2;
while (i1 < s1_len)
row[i1] = ++i1;
while (i2 < s2_len) {
c2 = s2.charCodeAt(i2);
a = i2;
++i2;
b = i2;
for (i1 = 0; i1 < s1_len; ++i1) {
c = a + (s1.charCodeAt(i1) !== c2 ? 1 : 0);
a = row[i1];
b = b < a ? (b < c ? b + 1 : c) : (a < c ? a + 1 : c);
row[i1] = b;
}
}
return b;
} else {
return s1_len + s2_len;
}
}
};
})();
function initSearch(rawSearchIndex) {
var currentResults, index, searchIndex;
var MAX_LEV_DISTANCE = 3;
var params = getQueryStringParams();
// Populate search bar with query string search term when provided,
// but only if the input bar is empty. This avoid the obnoxious issue
// where you start trying to do a search, and the index loads, and
// suddenly your search is gone!
if ($(".search-input")[0].value === "") {
$(".search-input")[0].value = params.search || '';
}
/**
* Executes the query and builds an index of results
* @param {[Object]} query [The user query]
* @param {[type]} max [The maximum results returned]
* @param {[type]} searchWords [The list of search words to query
* against]
* @return {[type]} [A search index of results]
*/
function execQuery(query, max, searchWords) {
var valLower = query.query.toLowerCase(),
val = valLower,
typeFilter = itemTypeFromName(query.type),
results = [],
split = valLower.split("::");
//remove empty keywords
for (var j = 0; j < split.length; ++j) {
split[j].toLowerCase();
if (split[j] === "") {
split.splice(j, 1);
}
}
// quoted values mean literal search
var nSearchWords = searchWords.length;
if ((val.charAt(0) === "\"" || val.charAt(0) === "'") &&
val.charAt(val.length - 1) === val.charAt(0))
{
val = val.substr(1, val.length - 2);
for (var i = 0; i < nSearchWords; ++i) {
if (searchWords[i] === val) {
// filter type: ... queries
if (typeFilter < 0 || typeFilter === searchIndex[i].ty) {
results.push({id: i, index: -1});
}
}
if (results.length === max) {
break;
}
}
// searching by type
} else if (val.search("->") > -1) {
var trimmer = function (s) { return s.trim(); };
var parts = val.split("->").map(trimmer);
var input = parts[0];
// sort inputs so that order does not matter
var inputs = input.split(",").map(trimmer).sort();
var output = parts[1];
for (var i = 0; i < nSearchWords; ++i) {
var type = searchIndex[i].type;
if (!type) {
continue;
}
// sort index inputs so that order does not matter
var typeInputs = type.inputs.map(function (input) {
return input.name;
}).sort();
// allow searching for void (no output) functions as well
var typeOutput = type.output ? type.output.name : "";
if (inputs.toString() === typeInputs.toString() &&
output == typeOutput) {
results.push({id: i, index: -1, dontValidate: true});
}
}
} else {
// gather matching search results up to a certain maximum
val = val.replace(/\_/g, "");
for (var i = 0; i < split.length; ++i) {
for (var j = 0; j < nSearchWords; ++j) {
var lev_distance;
if (searchWords[j].indexOf(split[i]) > -1 ||
searchWords[j].indexOf(val) > -1 ||
searchWords[j].replace(/_/g, "").indexOf(val) > -1)
{
// filter type: ... queries
if (typeFilter < 0 || typeFilter === searchIndex[j].ty) {
results.push({
id: j,
index: searchWords[j].replace(/_/g, "").indexOf(val),
lev: 0,
});
}
} else if (
(lev_distance = levenshtein(searchWords[j], val)) <=
MAX_LEV_DISTANCE) {
if (typeFilter < 0 || typeFilter === searchIndex[j].ty) {
results.push({
id: j,
index: 0,
// we want lev results to go lower than others
lev: lev_distance,
});
}
}
if (results.length === max) {
break;
}
}
}
}
var nresults = results.length;
for (var i = 0; i < nresults; ++i) {
results[i].word = searchWords[results[i].id];
results[i].item = searchIndex[results[i].id] || {};
}
// if there are no results then return to default and fail
if (results.length === 0) {
return [];
}
results.sort(function(aaa, bbb) {
var a, b;
// Sort by non levenshtein results and then levenshtein results by the distance
// (less changes required to match means higher rankings)
a = (aaa.lev);
b = (bbb.lev);
if (a !== b) return a - b;
// sort by crate (non-current crate goes later)
a = (aaa.item.crate !== window.currentCrate);
b = (bbb.item.crate !== window.currentCrate);
if (a !== b) return a - b;
// sort by exact match (mismatch goes later)
a = (aaa.word !== valLower);
b = (bbb.word !== valLower);
if (a !== b) return a - b;
// sort by item name length (longer goes later)
a = aaa.word.length;
b = bbb.word.length;
if (a !== b) return a - b;
// sort by item name (lexicographically larger goes later)
a = aaa.word;
b = bbb.word;
if (a !== b) return (a > b ? +1 : -1);
// sort by index of keyword in item name (no literal occurrence goes later)
a = (aaa.index < 0);
b = (bbb.index < 0);
if (a !== b) return a - b;
// (later literal occurrence, if any, goes later)
a = aaa.index;
b = bbb.index;
if (a !== b) return a - b;
// sort by description (no description goes later)
a = (aaa.item.desc === '');
b = (bbb.item.desc === '');
if (a !== b) return a - b;
// sort by type (later occurrence in `itemTypes` goes later)
a = aaa.item.ty;
b = bbb.item.ty;
if (a !== b) return a - b;
// sort by path (lexicographically larger goes later)
a = aaa.item.path;
b = bbb.item.path;
if (a !== b) return (a > b ? +1 : -1);
// que sera, sera
return 0;
});
// remove duplicates, according to the data provided
for (var i = results.length - 1; i > 0; i -= 1) {
if (results[i].word === results[i - 1].word &&
results[i].item.ty === results[i - 1].item.ty &&
results[i].item.path === results[i - 1].item.path &&
(results[i].item.parent || {}).name === (results[i - 1].item.parent || {}).name)
{
results[i].id = -1;
}
}
for (var i = 0; i < results.length; ++i) {
var result = results[i],
name = result.item.name.toLowerCase(),
path = result.item.path.toLowerCase(),
parent = result.item.parent;
// this validation does not make sense when searching by types
if (result.dontValidate) {
continue;
}
var valid = validateResult(name, path, split, parent);
if (!valid) {
result.id = -1;
}
}
return results;
}
/**
* Validate performs the following boolean logic. For example:
* "File::open" will give IF A PARENT EXISTS => ("file" && "open")
* exists in (name || path || parent) OR => ("file" && "open") exists in
* (name || path )
*
* This could be written functionally, but I wanted to minimise
* functions on stack.
*
* @param {[string]} name [The name of the result]
* @param {[string]} path [The path of the result]
* @param {[string]} keys [The keys to be used (["file", "open"])]
* @param {[object]} parent [The parent of the result]
* @return {[boolean]} [Whether the result is valid or not]
*/
function validateResult(name, path, keys, parent) {
for (var i=0; i < keys.length; ++i) {
// each check is for validation so we negate the conditions and invalidate
if (!(
// check for an exact name match
name.toLowerCase().indexOf(keys[i]) > -1 ||
// then an exact path match
path.toLowerCase().indexOf(keys[i]) > -1 ||
// next if there is a parent, check for exact parent match
(parent !== undefined &&
parent.name.toLowerCase().indexOf(keys[i]) > -1) ||
// lastly check to see if the name was a levenshtein match
levenshtein(name.toLowerCase(), keys[i]) <=
MAX_LEV_DISTANCE)) {
return false;
}
}
return true;
}
function getQuery() {
var matches, type, query, raw = $('.search-input').val();
query = raw;
matches = query.match(/^(fn|mod|struct|enum|trait|t(ype)?d(ef)?)\s*:\s*/i);
if (matches) {
type = matches[1].replace(/^td$/, 'typedef')
.replace(/^tdef$/, 'typedef')
.replace(/^typed$/, 'typedef');
query = query.substring(matches[0].length);
}
return {
raw: raw,
query: query,
type: type,
id: query + type,
};
}
function initSearchNav() {
var hoverTimeout, $results = $('.search-results .result');
$results.on('click', function() {
var dst = $(this).find('a')[0];
if (window.location.pathname == dst.pathname) {
$('#search').addClass('hidden');
$('#main').removeClass('hidden');
document.location.href = dst.href;
}
}).on('mouseover', function() {
var $el = $(this);
clearTimeout(hoverTimeout);
hoverTimeout = setTimeout(function() {
$results.removeClass('highlighted');
$el.addClass('highlighted');
}, 20);
});
$(document).off('keydown.searchnav');
$(document).on('keydown.searchnav', function(e) {
var $active = $results.filter('.highlighted');
if (e.which === 38) { // up
e.preventDefault();
if (!$active.length || !$active.prev()) {
return;
}
$active.prev().addClass('highlighted');
$active.removeClass('highlighted');
} else if (e.which === 40) { // down
e.preventDefault();
if (!$active.length) {
$results.first().addClass('highlighted');
} else if ($active.next().length) {
$active.next().addClass('highlighted');
$active.removeClass('highlighted');
}
} else if (e.which === 13) { // return
e.preventDefault();
if ($active.length) {
document.location.href = $active.find('a').prop('href');
}
} else {
$active.removeClass('highlighted');
}
});
}
function escape(content) {
return $('<h1/>').text(content).html();
}
function showResults(results) {
var output, shown, query = getQuery();
currentResults = query.id;
output = '<h1>Results for ' + escape(query.query) +
(query.type ? ' (type: ' + escape(query.type) + ')' : '') + '</h1>';
output += '<table class="search-results">';
if (results.length > 0) {
shown = [];
results.forEach(function(item) {
var name, type, href, displayPath;
if (shown.indexOf(item) !== -1) {
return;
}
shown.push(item);
name = item.name;
type = itemTypes[item.ty];
if (type === 'mod') {
displayPath = item.path + '::';
href = rootPath + item.path.replace(/::/g, '/') + '/' +
name + '/index.html';
} else if (type === 'static' || type === 'reexport') {
displayPath = item.path + '::';
href = rootPath + item.path.replace(/::/g, '/') +
'/index.html';
} else if (item.parent !== undefined) {
var myparent = item.parent;
var anchor = '#' + type + '.' + name;
displayPath = item.path + '::' + myparent.name + '::';
href = rootPath + item.path.replace(/::/g, '/') +
'/' + itemTypes[myparent.ty] +
'.' + myparent.name +
'.html' + anchor;
} else {
displayPath = item.path + '::';
href = rootPath + item.path.replace(/::/g, '/') +
'/' + type + '.' + name + '.html';
}
output += '<tr class="' + type + ' result"><td>' +
'<a href="' + href + '">' +
displayPath + '<span class="' + type + '">' +
name + '</span></a></td><td>' +
'<a href="' + href + '">' +
'<span class="desc">' + item.desc +
'&nbsp;</span></a></td></tr>';
});
} else {
output += 'No results :( <a href="https://duckduckgo.com/?q=' +
encodeURIComponent('rust ' + query.query) +
'">Try on DuckDuckGo?</a>';
}
output += "</p>";
$('#main.content').addClass('hidden');
$('#search.content').removeClass('hidden').html(output);
$('#search .desc').width($('#search').width() - 40 -
$('#search td:first-child').first().width());
initSearchNav();
}
function search(e) {
var query,
filterdata = [],
obj, i, len,
results = [],
maxResults = 200,
resultIndex;
var params = getQueryStringParams();
query = getQuery();
if (e) {
e.preventDefault();
}
if (!query.query || query.id === currentResults) {
return;
}
// Because searching is incremental by character, only the most
// recent search query is added to the browser history.
if (browserSupportsHistoryApi()) {
if (!history.state && !params.search) {
history.pushState(query, "", "?search=" +
encodeURIComponent(query.raw));
} else {
history.replaceState(query, "", "?search=" +
encodeURIComponent(query.raw));
}
}
resultIndex = execQuery(query, 20000, index);
len = resultIndex.length;
for (i = 0; i < len; ++i) {
if (resultIndex[i].id > -1) {
obj = searchIndex[resultIndex[i].id];
filterdata.push([obj.name, obj.ty, obj.path, obj.desc]);
results.push(obj);
}
if (results.length >= maxResults) {
break;
}
}
showResults(results);
}
function itemTypeFromName(typename) {
for (var i = 0; i < itemTypes.length; ++i) {
if (itemTypes[i] === typename) return i;
}
return -1;
}
function buildIndex(rawSearchIndex) {
searchIndex = [];
var searchWords = [];
for (var crate in rawSearchIndex) {
if (!rawSearchIndex.hasOwnProperty(crate)) { continue }
// an array of [(Number) item type,
// (String) name,
// (String) full path or empty string for previous path,
// (String) description,
// (Number | null) the parent path index to `paths`]
// (Object | null) the type of the function (if any)
var items = rawSearchIndex[crate].items;
// an array of [(Number) item type,
// (String) name]
var paths = rawSearchIndex[crate].paths;
// convert `paths` into an object form
var len = paths.length;
for (var i = 0; i < len; ++i) {
paths[i] = {ty: paths[i][0], name: paths[i][1]};
}
// convert `items` into an object form, and construct word indices.
//
// before any analysis is performed lets gather the search terms to
// search against apart from the rest of the data. This is a quick
// operation that is cached for the life of the page state so that
// all other search operations have access to this cached data for
// faster analysis operations
var len = items.length;
var lastPath = "";
for (var i = 0; i < len; ++i) {
var rawRow = items[i];
var row = {crate: crate, ty: rawRow[0], name: rawRow[1],
path: rawRow[2] || lastPath, desc: rawRow[3],
parent: paths[rawRow[4]], type: rawRow[5]};
searchIndex.push(row);
if (typeof row.name === "string") {
var word = row.name.toLowerCase();
searchWords.push(word);
} else {
searchWords.push("");
}
lastPath = row.path;
}
}
return searchWords;
}
function startSearch() {
var keyUpTimeout;
$('.do-search').on('click', search);
$('.search-input').on('keyup', function() {
clearTimeout(keyUpTimeout);
keyUpTimeout = setTimeout(search, 500);
});
// Push and pop states are used to add search results to the browser
// history.
if (browserSupportsHistoryApi()) {
$(window).on('popstate', function(e) {
var params = getQueryStringParams();
// When browsing back from search results the main page
// visibility must be reset.
if (!params.search) {
$('#main.content').removeClass('hidden');
$('#search.content').addClass('hidden');
}
// When browsing forward to search results the previous
// search will be repeated, so the currentResults are
// cleared to ensure the search is successful.
currentResults = null;
// Synchronize search bar with query string state and
// perform the search. This will empty the bar if there's
// nothing there, which lets you really go back to a
// previous state with nothing in the bar.
$('.search-input').val(params.search);
// Some browsers fire 'onpopstate' for every page load
// (Chrome), while others fire the event only when actually
// popping a state (Firefox), which is why search() is
// called both here and at the end of the startSearch()
// function.
search();
});
}
search();
}
function plainSummaryLine(markdown) {
var str = markdown.replace(/\n/g, ' ')
str = str.replace(/'/g, "\'")
str = str.replace(/^#+? (.+?)/, "$1")
str = str.replace(/\[(.*?)\]\(.*?\)/g, "$1")
str = str.replace(/\[(.*?)\]\[.*?\]/g, "$1")
return str;
}
index = buildIndex(rawSearchIndex);
startSearch();
// Draw a convenient sidebar of known crates if we have a listing
if (rootPath == '../') {
var sidebar = $('.sidebar');
var div = $('<div>').attr('class', 'block crate');
div.append($('<h2>').text('Crates'));
var crates = [];
for (var crate in rawSearchIndex) {
if (!rawSearchIndex.hasOwnProperty(crate)) { continue }
crates.push(crate);
}
crates.sort();
for (var i = 0; i < crates.length; ++i) {
var klass = 'crate';
if (crates[i] == window.currentCrate) {
klass += ' current';
}
if (rawSearchIndex[crates[i]].items[0]) {
var desc = rawSearchIndex[crates[i]].items[0][3];
div.append($('<a>', {'href': '../' + crates[i] + '/index.html',
'title': plainSummaryLine(desc),
'class': klass}).text(crates[i]));
}
}
sidebar.append(div);
}
}
window.initSearch = initSearch;
// delayed sidebar rendering.
function initSidebarItems(items) {
var sidebar = $('.sidebar');
var current = window.sidebarCurrent;
function block(shortty, longty) {
var filtered = items[shortty];
if (!filtered) return;
var div = $('<div>').attr('class', 'block ' + shortty);
div.append($('<h2>').text(longty));
for (var i = 0; i < filtered.length; ++i) {
var item = filtered[i];
var name = item[0];
var desc = item[1]; // can be null
var klass = shortty;
if (name === current.name && shortty == current.ty) {
klass += ' current';
}
var path;
if (shortty === 'mod') {
path = name + '/index.html';
} else {
path = shortty + '.' + name + '.html';
}
div.append($('<a>', {'href': current.relpath + path,
'title': desc,
'class': klass}).text(name));
}
sidebar.append(div);
}
block("mod", "Modules");
block("struct", "Structs");
block("enum", "Enums");
block("trait", "Traits");
block("fn", "Functions");
block("macro", "Macros");
}
window.initSidebarItems = initSidebarItems;
window.register_implementors = function(imp) {
var list = $('#implementors-list');
var libs = Object.getOwnPropertyNames(imp);
for (var i = 0; i < libs.length; ++i) {
if (libs[i] == currentCrate) continue;
var structs = imp[libs[i]];
for (var j = 0; j < structs.length; ++j) {
var code = $('<code>').append(structs[j]);
$.each(code.find('a'), function(idx, a) {
var href = $(a).attr('href');
if (href && href.indexOf('http') !== 0) {
$(a).attr('href', rootPath + href);
}
});
var li = $('<li>').append(code);
list.append(li);
}
}
};
if (window.pending_implementors) {
window.register_implementors(window.pending_implementors);
}
// See documentation in html/render.rs for what this is doing.
var query = getQueryStringParams();
if (query['gotosrc']) {
window.location = $('#src-' + query['gotosrc']).attr('href');
}
if (query['gotomacrosrc']) {
window.location = $('.srclink').attr('href');
}
function labelForToggleButton(sectionIsCollapsed) {
if (sectionIsCollapsed) {
// button will expand the section
return "+";
} else {
// button will collapse the section
// note that this text is also set in the HTML template in render.rs
return "\u2212"; // "\u2212" is '−' minus sign
}
}
$("#toggle-all-docs").on("click", function() {
var toggle = $("#toggle-all-docs");
if (toggle.hasClass("will-expand")) {
toggle.removeClass("will-expand");
toggle.children(".inner").text(labelForToggleButton(false));
toggle.attr("title", "collapse all docs");
$(".docblock").show();
$(".toggle-label").hide();
$(".toggle-wrapper").removeClass("collapsed");
$(".collapse-toggle").children(".inner").text(labelForToggleButton(false));
} else {
toggle.addClass("will-expand");
toggle.children(".inner").text(labelForToggleButton(true));
toggle.attr("title", "expand all docs");
$(".docblock").hide();
$(".toggle-label").show();
$(".toggle-wrapper").addClass("collapsed");
$(".collapse-toggle").children(".inner").text(labelForToggleButton(true));
}
});
$(document).on("click", ".collapse-toggle", function() {
var toggle = $(this);
var relatedDoc = toggle.parent().next();
if (relatedDoc.is(".stability")) {
relatedDoc = relatedDoc.next();
}
if (relatedDoc.is(".docblock")) {
if (relatedDoc.is(":visible")) {
relatedDoc.slideUp({duration:'fast', easing:'linear'});
toggle.parent(".toggle-wrapper").addClass("collapsed");
toggle.children(".inner").text(labelForToggleButton(true));
toggle.children(".toggle-label").fadeIn();
} else {
relatedDoc.slideDown({duration:'fast', easing:'linear'});
toggle.parent(".toggle-wrapper").removeClass("collapsed");
toggle.children(".inner").text(labelForToggleButton(false));
toggle.children(".toggle-label").hide();
}
}
});
$(function() {
var toggle = $("<a/>", {'href': 'javascript:void(0)', 'class': 'collapse-toggle'})
.html("[<span class='inner'></span>]");
toggle.children(".inner").text(labelForToggleButton(false));
$(".method").each(function() {
if ($(this).next().is(".docblock") ||
($(this).next().is(".stability") && $(this).next().next().is(".docblock"))) {
$(this).children().first().after(toggle.clone());
}
});
var mainToggle =
$(toggle).append(
$('<span/>', {'class': 'toggle-label'})
.css('display', 'none')
.html('&nbsp;Expand&nbsp;description'));
var wrapper = $("<div class='toggle-wrapper'>").append(mainToggle);
$("#main > .docblock").before(wrapper);
});
$('pre.line-numbers').on('click', 'span', function() {
var prev_id = 0;
function set_fragment(name) {
if (history.replaceState) {
history.replaceState(null, null, '#' + name);
$(window).trigger('hashchange');
} else {
location.replace('#' + name);
}
}
return function(ev) {
var cur_id = parseInt(ev.target.id);
if (ev.shiftKey && prev_id) {
if (prev_id > cur_id) {
var tmp = prev_id;
prev_id = cur_id;
cur_id = tmp;
}
set_fragment(prev_id + '-' + cur_id);
} else {
prev_id = cur_id;
set_fragment(cur_id);
}
};
}());
}());

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normalize.css
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/*! normalize.css v3.0.0 | MIT License | git.io/normalize */html{font-family:sans-serif;-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%}body{margin:0}article,aside,details,figcaption,figure,footer,header,hgroup,main,nav,section,summary{display:block}audio,canvas,progress,video{display:inline-block;vertical-align:baseline}audio:not([controls]){display:none;height:0}[hidden],template{display:none}a{background:transparent}a:active,a:hover{outline:0}abbr[title]{border-bottom:1px dotted}b,strong{font-weight:bold}dfn{font-style:italic}h1{font-size:2em;margin:.67em 0}mark{background:#ff0;color:#000}small{font-size:80%}sub,sup{font-size:75%;line-height:0;position:relative;vertical-align:baseline}sup{top:-0.5em}sub{bottom:-0.25em}img{border:0}svg:not(:root){overflow:hidden}figure{margin:1em 40px}hr{-moz-box-sizing:content-box;box-sizing:content-box;height:0}pre{overflow:auto}code,kbd,pre,samp{font-family:monospace,monospace;font-size:1em}button,input,optgroup,select,textarea{color:inherit;font:inherit;margin:0}button{overflow:visible}button,select{text-transform:none}button,html input[type="button"],input[type="reset"],input[type="submit"]{-webkit-appearance:button;cursor:pointer}button[disabled],html input[disabled]{cursor:default}button::-moz-focus-inner,input::-moz-focus-inner{border:0;padding:0}input{line-height:normal}input[type="checkbox"],input[type="radio"]{box-sizing:border-box;padding:0}input[type="number"]::-webkit-inner-spin-button,input[type="number"]::-webkit-outer-spin-button{height:auto}input[type="search"]{-webkit-appearance:textfield;-moz-box-sizing:content-box;-webkit-box-sizing:content-box;box-sizing:content-box}input[type="search"]::-webkit-search-cancel-button,input[type="search"]::-webkit-search-decoration{-webkit-appearance:none}fieldset{border:1px solid silver;margin:0 2px;padding:.35em .625em .75em}legend{border:0;padding:0}textarea{overflow:auto}optgroup{font-weight:bold}table{border-collapse:collapse;border-spacing:0}td,th{padding:0}

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playpen.js
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// Copyright 2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
/*jslint browser: true, es5: true */
/*globals $: true, rootPath: true */
(function() {
if (window.playgroundUrl) {
$('pre.rust').hover(function() {
var a = $('<a>').text('⇱').attr('class', 'test-arrow');
var code = $(this).prev(".rusttest").text();
a.attr('href', window.playgroundUrl + '?code=' +
encodeURIComponent(code));
a.attr('target', '_blank');
$(this).append(a);
}, function() {
$(this).find('a.test-arrow').remove();
});
}
}());

4
search-index.js
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src/complex/lib.rs.html
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="generator" content="rustdoc">
<meta name="description" content="Source to the Rust file `/home/travis/.cargo/registry/src/github.com-1ecc6299db9ec823/complex-0.7.5/src/lib.rs`.">
<meta name="keywords" content="rust, rustlang, rust-lang">
<title>lib.rs.html -- source</title>
<link rel="stylesheet" type="text/css" href="../../main.css">
</head>
<body class="rustdoc">
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things.
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<![endif]-->
<section class="sidebar">
</section>
<nav class="sub">
<form class="search-form js-only">
<div class="search-container">
<input class="search-input" name="search"
autocomplete="off"
placeholder="Click or press 'S' to search, '?' for more options..."
type="search">
</div>
</form>
</nav>
<section id='main' class="content source"><pre class="line-numbers"><span id="1"> 1</span>
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</pre><pre class='rust '>
<span class='doccomment'>//! [Complex numbers][1].</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! [1]: https://en.wikipedia.org/wiki/Complex_number</span>
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>fmt</span>::<span class='ident'>Debug</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>ops</span>::{<span class='ident'>Add</span>, <span class='ident'>Div</span>, <span class='ident'>Mul</span>, <span class='ident'>Neg</span>, <span class='ident'>Sub</span>};
<span class='doccomment'>/// A number.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Number</span>: <span class='ident'>Add</span><span class='op'>&lt;</span><span class='ident'>Output</span><span class='op'>=</span><span class='kw'>Self</span><span class='op'>&gt;</span> <span class='op'>+</span>
<span class='ident'>Div</span><span class='op'>&lt;</span><span class='ident'>Output</span><span class='op'>=</span><span class='kw'>Self</span><span class='op'>&gt;</span> <span class='op'>+</span>
<span class='ident'>Mul</span><span class='op'>&lt;</span><span class='ident'>Output</span><span class='op'>=</span><span class='kw'>Self</span><span class='op'>&gt;</span> <span class='op'>+</span>
<span class='ident'>Neg</span><span class='op'>&lt;</span><span class='ident'>Output</span><span class='op'>=</span><span class='kw'>Self</span><span class='op'>&gt;</span> <span class='op'>+</span>
<span class='ident'>Sub</span><span class='op'>&lt;</span><span class='ident'>Output</span><span class='op'>=</span><span class='kw'>Self</span><span class='op'>&gt;</span> <span class='op'>+</span>
<span class='ident'>Copy</span> <span class='op'>+</span> <span class='ident'>Debug</span> <span class='op'>+</span> <span class='ident'>PartialEq</span> {
}
<span class='doccomment'>/// A real number.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Real</span>: <span class='ident'>Number</span> {
}
<span class='doccomment'>/// A complex number.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Complex</span>: <span class='ident'>Number</span> {
<span class='doccomment'>/// A real number.</span>
<span class='kw'>type</span> <span class='ident'>Real</span>: <span class='ident'>Real</span>;
<span class='doccomment'>/// Create a complex number from a real and an imaginary part.</span>
<span class='kw'>fn</span> <span class='ident'>new</span>(<span class='ident'>Self</span>::<span class='ident'>Real</span>, <span class='ident'>Self</span>::<span class='ident'>Real</span>) <span class='op'>-&gt;</span> <span class='kw'>Self</span>;
<span class='doccomment'>/// Create a complex number from a modulus and an argument.</span>
<span class='kw'>fn</span> <span class='ident'>from_polar</span>(<span class='ident'>Self</span>::<span class='ident'>Real</span>, <span class='ident'>Self</span>::<span class='ident'>Real</span>) <span class='op'>-&gt;</span> <span class='kw'>Self</span>;
<span class='doccomment'>/// Return the real part.</span>
<span class='kw'>fn</span> <span class='ident'>re</span>(<span class='kw-2'>&amp;</span><span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Real</span>;
<span class='doccomment'>/// Return the real part as a mutable reference.</span>
<span class='kw'>fn</span> <span class='ident'>re_mut</span>(<span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> <span class='ident'>Self</span>::<span class='ident'>Real</span>;
<span class='doccomment'>/// Return the imaginary part.</span>
<span class='kw'>fn</span> <span class='ident'>im</span>(<span class='kw-2'>&amp;</span><span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Real</span>;
<span class='doccomment'>/// Return the imaginary part as a mutable reference.</span>
<span class='kw'>fn</span> <span class='ident'>im_mut</span>(<span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> <span class='ident'>Self</span>::<span class='ident'>Real</span>;
<span class='doccomment'>/// Compute the modulus.</span>
<span class='kw'>fn</span> <span class='ident'>abs</span>(<span class='kw-2'>&amp;</span><span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Real</span>;
<span class='doccomment'>/// Compute the argument.</span>
<span class='kw'>fn</span> <span class='ident'>arg</span>(<span class='kw-2'>&amp;</span><span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Real</span>;
<span class='doccomment'>/// Compute the modulus and the argument.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>to_polar</span>(<span class='kw-2'>&amp;</span><span class='self'>self</span>) <span class='op'>-&gt;</span> (<span class='ident'>Self</span>::<span class='ident'>Real</span>, <span class='ident'>Self</span>::<span class='ident'>Real</span>) {
(<span class='self'>self</span>.<span class='ident'>abs</span>(), <span class='self'>self</span>.<span class='ident'>arg</span>())
}
<span class='doccomment'>/// Compute the complex conjugate.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>conj</span>(<span class='kw-2'>&amp;</span><span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='kw'>Self</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>re</span>(), <span class='op'>-</span><span class='self'>self</span>.<span class='ident'>im</span>())
}
}
<span class='doccomment'>/// A complex number with 32-bit parts.</span>
<span class='attribute'>#[<span class='ident'>allow</span>(<span class='ident'>non_camel_case_types</span>)]</span>
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Clone</span>, <span class='ident'>Copy</span>, <span class='ident'>Debug</span>, <span class='ident'>PartialEq</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>c32</span>(<span class='kw'>pub</span> <span class='ident'>f32</span>, <span class='kw'>pub</span> <span class='ident'>f32</span>);
<span class='doccomment'>/// A complex number with 64-bit parts.</span>
<span class='attribute'>#[<span class='ident'>allow</span>(<span class='ident'>non_camel_case_types</span>)]</span>
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Clone</span>, <span class='ident'>Copy</span>, <span class='ident'>Debug</span>, <span class='ident'>PartialEq</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>c64</span>(<span class='kw'>pub</span> <span class='ident'>f64</span>, <span class='kw'>pub</span> <span class='ident'>f64</span>);
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>implement</span>(
(<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>:<span class='ident'>ident</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span>:<span class='ident'>ty</span>) <span class='op'>=&gt;</span> (
<span class='kw'>impl</span> <span class='ident'>Number</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
}
<span class='kw'>impl</span> <span class='ident'>Number</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span> {
}
<span class='kw'>impl</span> <span class='ident'>Real</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span> {
}
<span class='kw'>impl</span> <span class='ident'>Complex</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='kw'>type</span> <span class='ident'>Real</span> <span class='op'>=</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>new</span>(<span class='ident'>re</span>: <span class='ident'>Self</span>::<span class='ident'>Real</span>, <span class='ident'>im</span>: <span class='ident'>Self</span>::<span class='ident'>Real</span>) <span class='op'>-&gt;</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>(<span class='ident'>re</span>, <span class='ident'>im</span>)
}
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>from_polar</span>(<span class='ident'>abs</span>: <span class='ident'>Self</span>::<span class='ident'>Real</span>, <span class='ident'>arg</span>: <span class='ident'>Self</span>::<span class='ident'>Real</span>) <span class='op'>-&gt;</span> <span class='kw'>Self</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>(<span class='ident'>abs</span> <span class='op'>*</span> <span class='ident'>arg</span>.<span class='ident'>cos</span>(), <span class='ident'>abs</span> <span class='op'>*</span> <span class='ident'>arg</span>.<span class='ident'>sin</span>())
}
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>re</span>(<span class='kw-2'>&amp;</span><span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Real</span> {
<span class='self'>self</span>.<span class='number'>0</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>re_mut</span>(<span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> <span class='ident'>Self</span>::<span class='ident'>Real</span> {
<span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> <span class='self'>self</span>.<span class='number'>0</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>im</span>(<span class='kw-2'>&amp;</span><span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Real</span> {
<span class='self'>self</span>.<span class='number'>1</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>im_mut</span>(<span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> <span class='ident'>Self</span>::<span class='ident'>Real</span> {
<span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> <span class='self'>self</span>.<span class='number'>1</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>abs</span>(<span class='kw-2'>&amp;</span><span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Real</span> {
<span class='self'>self</span>.<span class='ident'>re</span>().<span class='ident'>hypot</span>(<span class='self'>self</span>.<span class='ident'>im</span>())
}
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>arg</span>(<span class='kw-2'>&amp;</span><span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Real</span> {
<span class='self'>self</span>.<span class='ident'>im</span>().<span class='ident'>atan2</span>(<span class='self'>self</span>.<span class='ident'>re</span>())
}
}
<span class='kw'>impl</span> <span class='ident'>Add</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='kw'>Self</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>add</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='kw'>Self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>re</span>() <span class='op'>+</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>(), <span class='self'>self</span>.<span class='ident'>im</span>() <span class='op'>+</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>())
}
}
<span class='kw'>impl</span> <span class='ident'>Add</span><span class='op'>&lt;</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span><span class='op'>&gt;</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='kw'>Self</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>add</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>re</span>() <span class='op'>+</span> <span class='ident'>rhs</span>, <span class='self'>self</span>.<span class='ident'>im</span>())
}
}
<span class='kw'>impl</span> <span class='ident'>Add</span><span class='op'>&lt;</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span><span class='op'>&gt;</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>add</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span> <span class='op'>+</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>(), <span class='ident'>rhs</span>.<span class='ident'>im</span>())
}
}
<span class='kw'>impl</span> <span class='ident'>Div</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='kw'>Self</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>div</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='kw'>Self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='kw'>let</span> <span class='ident'>denominator</span> <span class='op'>=</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>() <span class='op'>+</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>();
<span class='ident'>Complex</span>::<span class='ident'>new</span>((<span class='self'>self</span>.<span class='ident'>re</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>() <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>im</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>()) <span class='op'>/</span> <span class='ident'>denominator</span>,
(<span class='self'>self</span>.<span class='ident'>im</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>() <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>re</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>()) <span class='op'>/</span> <span class='ident'>denominator</span>)
}
}
<span class='kw'>impl</span> <span class='ident'>Div</span><span class='op'>&lt;</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span><span class='op'>&gt;</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='kw'>Self</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>div</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>re</span>() <span class='op'>/</span> <span class='ident'>rhs</span>, <span class='self'>self</span>.<span class='ident'>im</span>() <span class='op'>/</span> <span class='ident'>rhs</span>)
}
}
<span class='kw'>impl</span> <span class='ident'>Div</span><span class='op'>&lt;</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span><span class='op'>&gt;</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>div</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='kw'>let</span> <span class='ident'>denominator</span> <span class='op'>=</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>() <span class='op'>+</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>();
<span class='ident'>Complex</span>::<span class='ident'>new</span>((<span class='self'>self</span> <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>()) <span class='op'>/</span> <span class='ident'>denominator</span>, (<span class='op'>-</span><span class='self'>self</span> <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>()) <span class='op'>/</span> <span class='ident'>denominator</span>)
}
}
<span class='kw'>impl</span> <span class='ident'>Mul</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='kw'>Self</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='kw'>Self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>re</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>() <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>im</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>(),
<span class='self'>self</span>.<span class='ident'>im</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>() <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>re</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>())
}
}
<span class='kw'>impl</span> <span class='ident'>Mul</span><span class='op'>&lt;</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span><span class='op'>&gt;</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='kw'>Self</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>re</span>() <span class='op'>*</span> <span class='ident'>rhs</span>, <span class='self'>self</span>.<span class='ident'>im</span>() <span class='op'>*</span> <span class='ident'>rhs</span>)
}
}
<span class='kw'>impl</span> <span class='ident'>Mul</span><span class='op'>&lt;</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span><span class='op'>&gt;</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span> <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>(), <span class='self'>self</span> <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>())
}
}
<span class='kw'>impl</span> <span class='ident'>Neg</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='kw'>Self</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>neg</span>(<span class='self'>self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='op'>-</span><span class='self'>self</span>.<span class='ident'>re</span>(), <span class='op'>-</span><span class='self'>self</span>.<span class='ident'>im</span>())
}
}
<span class='kw'>impl</span> <span class='ident'>Sub</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='kw'>Self</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>sub</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='kw'>Self</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>re</span>() <span class='op'>-</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>(), <span class='self'>self</span>.<span class='ident'>im</span>() <span class='op'>-</span> <span class='ident'>rhs</span>.<span class='ident'>im</span>())
}
}
<span class='kw'>impl</span> <span class='ident'>Sub</span><span class='op'>&lt;</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span><span class='op'>&gt;</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='kw'>Self</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>sub</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>re</span>() <span class='op'>-</span> <span class='ident'>rhs</span>, <span class='self'>self</span>.<span class='ident'>im</span>())
}
}
<span class='kw'>impl</span> <span class='ident'>Sub</span><span class='op'>&lt;</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span><span class='op'>&gt;</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>real</span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>;
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>sub</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>complex</span>) <span class='op'>-&gt;</span> <span class='ident'>Self</span>::<span class='ident'>Output</span> {
<span class='ident'>Complex</span>::<span class='ident'>new</span>(<span class='self'>self</span> <span class='op'>-</span> <span class='ident'>rhs</span>.<span class='ident'>re</span>(), <span class='op'>-</span><span class='ident'>rhs</span>.<span class='ident'>im</span>())
}
}
);
);
<span class='macro'>implement</span><span class='macro'>!</span>(<span class='ident'>c32</span>, <span class='ident'>f32</span>);
<span class='macro'>implement</span><span class='macro'>!</span>(<span class='ident'>c64</span>, <span class='ident'>f64</span>);
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>test</span>)]</span>
<span class='kw'>mod</span> <span class='ident'>tests</span> {
<span class='kw'>use</span> {<span class='ident'>Complex</span>, <span class='ident'>c64</span>};
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>re_mut</span>() {
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>number</span> <span class='op'>=</span> <span class='ident'>c64</span>(<span class='number'>69.0</span>, <span class='number'>0.0</span>);
<span class='op'>*</span><span class='ident'>number</span>.<span class='ident'>re_mut</span>() <span class='op'>=</span> <span class='number'>42.0</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>number</span>, <span class='ident'>c64</span>(<span class='number'>42.0</span>, <span class='number'>0.0</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>im_mut</span>() {
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>number</span> <span class='op'>=</span> <span class='ident'>c64</span>(<span class='number'>0.0</span>, <span class='number'>69.0</span>);
<span class='op'>*</span><span class='ident'>number</span>.<span class='ident'>im_mut</span>() <span class='op'>=</span> <span class='number'>42.0</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>number</span>, <span class='ident'>c64</span>(<span class='number'>0.0</span>, <span class='number'>42.0</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>abs</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>4.0</span>, <span class='number'>3.0</span>).<span class='ident'>abs</span>(), <span class='number'>5.0</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>arg</span>() {
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='number'>0.0</span>).<span class='ident'>arg</span>(), <span class='number'>0.0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='number'>1.0</span>).<span class='ident'>arg</span>(), <span class='ident'>PI</span> <span class='op'>/</span> <span class='number'>4.0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>0.0</span>, <span class='number'>1.0</span>).<span class='ident'>arg</span>(), <span class='ident'>PI</span> <span class='op'>/</span> <span class='number'>2.0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='op'>-</span><span class='number'>1.0</span>, <span class='number'>0.0</span>).<span class='ident'>arg</span>(), <span class='ident'>PI</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>0.0</span>, <span class='op'>-</span><span class='number'>1.0</span>).<span class='ident'>arg</span>(), <span class='op'>-</span><span class='ident'>PI</span> <span class='op'>/</span> <span class='number'>2.0</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>conj</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>42.0</span>, <span class='number'>69.0</span>).<span class='ident'>conj</span>(), <span class='ident'>c64</span>(<span class='number'>42.0</span>, <span class='op'>-</span><span class='number'>69.0</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>add</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='op'>-</span><span class='number'>4.0</span>, <span class='number'>7.0</span>) <span class='op'>+</span> <span class='ident'>c64</span>(<span class='number'>5.0</span>, <span class='op'>-</span><span class='number'>10.0</span>), <span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='op'>-</span><span class='number'>3.0</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='op'>-</span><span class='number'>4.0</span>, <span class='number'>7.0</span>) <span class='op'>+</span> <span class='number'>5.0</span>, <span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='number'>7.0</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='number'>5.0</span> <span class='op'>+</span> <span class='ident'>c64</span>(<span class='op'>-</span><span class='number'>4.0</span>, <span class='number'>7.0</span>), <span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='number'>7.0</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>div</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>3.0</span>, <span class='op'>-</span><span class='number'>1.0</span>) <span class='op'>/</span> <span class='ident'>c64</span>(<span class='number'>2.0</span>, <span class='number'>7.0</span>), <span class='ident'>c64</span>(<span class='op'>-</span><span class='number'>1.0</span> <span class='op'>/</span> <span class='number'>53.0</span>, <span class='op'>-</span><span class='number'>23.0</span> <span class='op'>/</span> <span class='number'>53.0</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>3.0</span>, <span class='op'>-</span><span class='number'>1.0</span>) <span class='op'>/</span> <span class='number'>2.0</span>, <span class='ident'>c64</span>(<span class='number'>1.5</span>, <span class='op'>-</span><span class='number'>0.5</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='number'>2.0</span> <span class='op'>/</span> <span class='ident'>c64</span>(<span class='number'>3.0</span>, <span class='op'>-</span><span class='number'>1.0</span>), <span class='ident'>c64</span>(<span class='number'>0.6</span>, <span class='number'>0.2</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>4.0</span>, <span class='number'>1.0</span>) <span class='op'>*</span> <span class='ident'>c64</span>(<span class='number'>2.0</span>, <span class='number'>3.0</span>), <span class='ident'>c64</span>(<span class='number'>5.0</span>, <span class='number'>14.0</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>4.0</span>, <span class='number'>1.0</span>) <span class='op'>*</span> <span class='number'>2.0</span>, <span class='ident'>c64</span>(<span class='number'>8.0</span>, <span class='number'>2.0</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='number'>2.0</span> <span class='op'>*</span> <span class='ident'>c64</span>(<span class='number'>4.0</span>, <span class='number'>1.0</span>), <span class='ident'>c64</span>(<span class='number'>8.0</span>, <span class='number'>2.0</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>neg</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='op'>-</span><span class='ident'>c64</span>(<span class='number'>42.0</span>, <span class='number'>69.0</span>), <span class='ident'>c64</span>(<span class='number'>42.0</span>, <span class='number'>69.0</span>) <span class='op'>*</span> (<span class='op'>-</span><span class='number'>1.0</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>sub</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>4.0</span>, <span class='number'>12.0</span>) <span class='op'>-</span> <span class='ident'>c64</span>(<span class='number'>3.0</span>, <span class='op'>-</span><span class='number'>15.0</span>), <span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='number'>27.0</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>c64</span>(<span class='number'>4.0</span>, <span class='number'>12.0</span>) <span class='op'>-</span> <span class='number'>3.0</span>, <span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='number'>12.0</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='number'>3.0</span> <span class='op'>-</span> <span class='ident'>c64</span>(<span class='number'>4.0</span>, <span class='number'>12.0</span>), <span class='ident'>c64</span>(<span class='op'>-</span><span class='number'>1.0</span>, <span class='op'>-</span><span class='number'>12.0</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>size_of</span>() {
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>mem</span>::<span class='ident'>size_of</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>size_of</span>::<span class='op'>&lt;</span><span class='ident'>c64</span><span class='op'>&gt;</span>(), <span class='number'>2</span> <span class='op'>*</span> <span class='ident'>size_of</span>::<span class='op'>&lt;</span><span class='ident'>f64</span><span class='op'>&gt;</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>size_of</span>::<span class='op'>&lt;</span>[<span class='ident'>c64</span>; <span class='number'>42</span>]<span class='op'>&gt;</span>(), <span class='ident'>size_of</span>::<span class='op'>&lt;</span>[<span class='ident'>f64</span>; <span class='number'>2</span> <span class='op'>*</span> <span class='number'>42</span>]<span class='op'>&gt;</span>());
}
}
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</pre><pre class='rust '>
<span class='doccomment'>//! Transformation of complex data.</span>
<span class='comment'>// The implementation is based on:</span>
<span class='comment'>// http://www.librow.com/articles/article-10</span>
<span class='kw'>use</span> <span class='ident'>number</span>::<span class='ident'>c64</span>;
<span class='doccomment'>/// Perform the forward transform.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The number of points should be a power of two.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>forward</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> [<span class='ident'>c64</span>]) {
<span class='kw'>let</span> <span class='ident'>n</span> <span class='op'>=</span> <span class='macro'>power_of_two</span><span class='macro'>!</span>(<span class='ident'>data</span>);
<span class='ident'>rearrange</span>(<span class='ident'>data</span>, <span class='ident'>n</span>);
<span class='ident'>transform</span>(<span class='ident'>data</span>, <span class='ident'>n</span>, <span class='boolval'>false</span>);
}
<span class='doccomment'>/// Perform the backward transform.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The number of points should be a power of two.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>backward</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> [<span class='ident'>c64</span>]) {
<span class='kw'>let</span> <span class='ident'>n</span> <span class='op'>=</span> <span class='macro'>power_of_two</span><span class='macro'>!</span>(<span class='ident'>data</span>);
<span class='ident'>rearrange</span>(<span class='ident'>data</span>, <span class='ident'>n</span>);
<span class='ident'>transform</span>(<span class='ident'>data</span>, <span class='ident'>n</span>, <span class='boolval'>true</span>);
}
<span class='doccomment'>/// Perform the inverse transform.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The number of points should be a power of two.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>inverse</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> [<span class='ident'>c64</span>]) {
<span class='kw'>let</span> <span class='ident'>n</span> <span class='op'>=</span> <span class='macro'>power_of_two</span><span class='macro'>!</span>(<span class='ident'>data</span>);
<span class='ident'>rearrange</span>(<span class='ident'>data</span>, <span class='ident'>n</span>);
<span class='ident'>transform</span>(<span class='ident'>data</span>, <span class='ident'>n</span>, <span class='boolval'>true</span>);
<span class='ident'>scale</span>(<span class='ident'>data</span>, <span class='ident'>n</span>);
}
<span class='kw'>fn</span> <span class='ident'>rearrange</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> [<span class='ident'>c64</span>], <span class='ident'>n</span>: <span class='ident'>usize</span>) {
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>j</span> <span class='op'>=</span> <span class='number'>0</span>;
<span class='kw'>for</span> <span class='ident'>i</span> <span class='kw'>in</span> <span class='number'>0</span>..<span class='ident'>n</span> {
<span class='kw'>if</span> <span class='ident'>j</span> <span class='op'>&gt;</span> <span class='ident'>i</span> {
<span class='ident'>data</span>.<span class='ident'>swap</span>(<span class='ident'>i</span>, <span class='ident'>j</span>);
}
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>mask</span> <span class='op'>=</span> <span class='ident'>n</span> <span class='op'>&gt;&gt;</span> <span class='number'>1</span>;
<span class='kw'>while</span> <span class='ident'>j</span> <span class='kw-2'>&amp;</span> <span class='ident'>mask</span> <span class='op'>!=</span> <span class='number'>0</span> {
<span class='ident'>j</span> <span class='op'>&amp;=</span> <span class='op'>!</span><span class='ident'>mask</span>;
<span class='ident'>mask</span> <span class='op'>&gt;&gt;=</span> <span class='number'>1</span>;
}
<span class='ident'>j</span> <span class='op'>|=</span> <span class='ident'>mask</span>;
}
}
<span class='kw'>fn</span> <span class='ident'>transform</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> [<span class='ident'>c64</span>], <span class='ident'>n</span>: <span class='ident'>usize</span>, <span class='ident'>inverse</span>: <span class='ident'>bool</span>) {
<span class='kw'>let</span> <span class='ident'>sign</span> <span class='op'>=</span> <span class='kw'>if</span> <span class='ident'>inverse</span> { <span class='number'>1.0</span> } <span class='kw'>else</span> { <span class='op'>-</span><span class='number'>1.0</span> };
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>step</span> <span class='op'>=</span> <span class='number'>1</span>;
<span class='kw'>while</span> <span class='ident'>step</span> <span class='op'>&lt;</span> <span class='ident'>n</span> {
<span class='kw'>let</span> <span class='ident'>jump</span> <span class='op'>=</span> <span class='ident'>step</span> <span class='op'>&lt;&lt;</span> <span class='number'>1</span>;
<span class='kw'>let</span> (<span class='ident'>multiplier</span>, <span class='kw-2'>mut</span> <span class='ident'>factor</span>) <span class='op'>=</span> {
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span>;
<span class='kw'>let</span> <span class='ident'>theta</span> <span class='op'>=</span> <span class='ident'>sign</span> <span class='op'>*</span> <span class='ident'>PI</span> <span class='op'>/</span> <span class='ident'>step</span> <span class='kw'>as</span> <span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>sine</span> <span class='op'>=</span> (<span class='number'>0.5</span> <span class='op'>*</span> <span class='ident'>theta</span>).<span class='ident'>sin</span>();
(<span class='ident'>c64</span>(<span class='op'>-</span><span class='number'>2.0</span> <span class='op'>*</span> <span class='ident'>sine</span> <span class='op'>*</span> <span class='ident'>sine</span>, <span class='ident'>theta</span>.<span class='ident'>sin</span>()), <span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='number'>0.0</span>))
};
<span class='kw'>for</span> <span class='kw-2'>mut</span> <span class='ident'>i</span> <span class='kw'>in</span> <span class='number'>0</span>..<span class='ident'>step</span> {
<span class='kw'>while</span> <span class='ident'>i</span> <span class='op'>&lt;</span> <span class='ident'>n</span> {
<span class='kw'>let</span> <span class='ident'>j</span> <span class='op'>=</span> <span class='ident'>i</span> <span class='op'>+</span> <span class='ident'>step</span>;
<span class='kw'>let</span> <span class='ident'>product</span> <span class='op'>=</span> <span class='ident'>factor</span> <span class='op'>*</span> <span class='ident'>data</span>[<span class='ident'>j</span>];
<span class='ident'>data</span>[<span class='ident'>j</span>] <span class='op'>=</span> <span class='ident'>data</span>[<span class='ident'>i</span>] <span class='op'>-</span> <span class='ident'>product</span>;
<span class='ident'>data</span>[<span class='ident'>i</span>] <span class='op'>=</span> <span class='ident'>data</span>[<span class='ident'>i</span>] <span class='op'>+</span> <span class='ident'>product</span>;
<span class='ident'>i</span> <span class='op'>+=</span> <span class='ident'>jump</span>;
}
<span class='ident'>factor</span> <span class='op'>=</span> <span class='ident'>multiplier</span> <span class='op'>*</span> <span class='ident'>factor</span> <span class='op'>+</span> <span class='ident'>factor</span>;
}
<span class='ident'>step</span> <span class='op'>&lt;&lt;=</span> <span class='number'>1</span>;
}
}
<span class='kw'>fn</span> <span class='ident'>scale</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> [<span class='ident'>c64</span>], <span class='ident'>n</span>: <span class='ident'>usize</span>) {
<span class='kw'>let</span> <span class='ident'>factor</span> <span class='op'>=</span> <span class='number'>1.0</span> <span class='op'>/</span> <span class='ident'>n</span> <span class='kw'>as</span> <span class='ident'>f64</span>;
<span class='kw'>for</span> <span class='ident'>i</span> <span class='kw'>in</span> <span class='number'>0</span>..<span class='ident'>n</span> {
<span class='ident'>data</span>[<span class='ident'>i</span>] <span class='op'>=</span> <span class='ident'>data</span>[<span class='ident'>i</span>] <span class='op'>*</span> <span class='ident'>factor</span>;
}
}
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<section id='main' class="content source"><pre class="line-numbers"><span id="1"> 1</span>
<span id="2"> 2</span>
<span id="3"> 3</span>
<span id="4"> 4</span>
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<span id="18">18</span>
</pre><pre class='rust '>
<span class='doccomment'>//! [Discrete Fourier transform][1].</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! [1]: https://en.wikipedia.org/wiki/Discrete_Fourier_transform</span>
<span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>complex</span> <span class='kw'>as</span> <span class='ident'>number</span>;
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>power_of_two</span>(
(<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>data</span>:<span class='ident'>expr</span>) <span class='op'>=&gt;</span> ({
<span class='kw'>let</span> <span class='ident'>n</span> <span class='op'>=</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>data</span>.<span class='ident'>len</span>();
<span class='kw'>if</span> <span class='op'>!</span><span class='ident'>n</span>.<span class='ident'>is_power_of_two</span>() {
<span class='macro'>panic</span><span class='macro'>!</span>(<span class='string'>&quot;expected the number of points to be a power of two&quot;</span>);
}
<span class='ident'>n</span>
});
);
<span class='kw'>pub</span> <span class='kw'>mod</span> <span class='ident'>complex</span>;
<span class='kw'>pub</span> <span class='kw'>mod</span> <span class='ident'>real</span>;
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<section id='main' class="content source"><pre class="line-numbers"><span id="1"> 1</span>
<span id="2"> 2</span>
<span id="3"> 3</span>
<span id="4"> 4</span>
<span id="5"> 5</span>
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<span id="113">113</span>
</pre><pre class='rust '>
<span class='doccomment'>//! Transformation of real data.</span>
<span class='kw'>use</span> <span class='ident'>number</span>::{<span class='ident'>Complex</span>, <span class='ident'>c64</span>};
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>reinterpret</span>(
(<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>data</span>:<span class='ident'>ident</span>) <span class='op'>=&gt;</span> (<span class='kw'>unsafe</span> {
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>slice</span>::<span class='ident'>from_raw_parts_mut</span>;
<span class='kw'>let</span> <span class='ident'>n</span> <span class='op'>=</span> <span class='macro'>power_of_two</span><span class='macro'>!</span>(<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>data</span>);
(<span class='ident'>from_raw_parts_mut</span>(<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>data</span>.<span class='ident'>as_mut_ptr</span>() <span class='kw'>as</span> <span class='op'>*</span><span class='kw-2'>mut</span> _, <span class='ident'>n</span> <span class='op'>/</span> <span class='number'>2</span>), <span class='ident'>n</span> <span class='op'>/</span> <span class='number'>2</span>)
});
);
<span class='doccomment'>/// Perform the forward transform.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The number of points should be a power of two. The data are replaced by the</span>
<span class='doccomment'>/// positive frequency half of their complex Fourier transform. The real-valued</span>
<span class='doccomment'>/// first and last components of the complex transform are returned as elements</span>
<span class='doccomment'>/// `data[0]` and `data[1]`, respectively.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ## References</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// 1. William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P.</span>
<span class='doccomment'>/// Flannery, “Numerical Recipes 3rd Edition: The Art of Scientific</span>
<span class='doccomment'>/// Computing,” Cambridge University Press, 2007.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>forward</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> [<span class='ident'>f64</span>]) {
<span class='kw'>let</span> (<span class='ident'>data</span>, <span class='ident'>n</span>) <span class='op'>=</span> <span class='macro'>reinterpret</span><span class='macro'>!</span>(<span class='ident'>data</span>);
::<span class='ident'>complex</span>::<span class='ident'>forward</span>(<span class='ident'>data</span>);
<span class='ident'>compose</span>(<span class='ident'>data</span>, <span class='ident'>n</span>, <span class='boolval'>false</span>);
}
<span class='doccomment'>/// Perform the backward transform.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The number of points should be a power of two. The data should be packed as</span>
<span class='doccomment'>/// described in `real::forward`.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>backward</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> [<span class='ident'>f64</span>]) {
<span class='kw'>let</span> (<span class='ident'>data</span>, <span class='ident'>n</span>) <span class='op'>=</span> <span class='macro'>reinterpret</span><span class='macro'>!</span>(<span class='ident'>data</span>);
<span class='ident'>compose</span>(<span class='ident'>data</span>, <span class='ident'>n</span>, <span class='boolval'>true</span>);
::<span class='ident'>complex</span>::<span class='ident'>backward</span>(<span class='ident'>data</span>);
}
<span class='doccomment'>/// Perform the inverse transform.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The number of points should be a power of two. The data should be packed as</span>
<span class='doccomment'>/// described in `real::forward`.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>inverse</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> [<span class='ident'>f64</span>]) {
<span class='kw'>let</span> (<span class='ident'>data</span>, <span class='ident'>n</span>) <span class='op'>=</span> <span class='macro'>reinterpret</span><span class='macro'>!</span>(<span class='ident'>data</span>);
<span class='ident'>compose</span>(<span class='ident'>data</span>, <span class='ident'>n</span>, <span class='boolval'>true</span>);
::<span class='ident'>complex</span>::<span class='ident'>inverse</span>(<span class='ident'>data</span>);
}
<span class='doccomment'>/// Unpack a compressed representation produced by `real::forward`.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>unpack</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span>[<span class='ident'>f64</span>]) <span class='op'>-&gt;</span> <span class='ident'>Vec</span><span class='op'>&lt;</span><span class='ident'>c64</span><span class='op'>&gt;</span> {
<span class='kw'>let</span> <span class='ident'>n</span> <span class='op'>=</span> <span class='macro'>power_of_two</span><span class='macro'>!</span>(<span class='ident'>data</span>);
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>cdata</span> <span class='op'>=</span> <span class='ident'>Vec</span>::<span class='ident'>with_capacity</span>(<span class='ident'>n</span>);
<span class='kw'>unsafe</span> { <span class='ident'>cdata</span>.<span class='ident'>set_len</span>(<span class='ident'>n</span>) };
<span class='ident'>cdata</span>[<span class='number'>0</span>] <span class='op'>=</span> <span class='ident'>c64</span>(<span class='ident'>data</span>[<span class='number'>0</span>], <span class='number'>0.0</span>);
<span class='kw'>for</span> <span class='ident'>i</span> <span class='kw'>in</span> <span class='number'>1</span>..(<span class='ident'>n</span> <span class='op'>/</span> <span class='number'>2</span>) {
<span class='ident'>cdata</span>[<span class='ident'>i</span>] <span class='op'>=</span> <span class='ident'>c64</span>(<span class='ident'>data</span>[<span class='number'>2</span> <span class='op'>*</span> <span class='ident'>i</span>], <span class='ident'>data</span>[<span class='number'>2</span> <span class='op'>*</span> <span class='ident'>i</span> <span class='op'>+</span> <span class='number'>1</span>]);
}
<span class='ident'>cdata</span>[<span class='ident'>n</span> <span class='op'>/</span> <span class='number'>2</span>] <span class='op'>=</span> <span class='ident'>c64</span>(<span class='ident'>data</span>[<span class='number'>1</span>], <span class='number'>0.0</span>);
<span class='kw'>for</span> <span class='ident'>i</span> <span class='kw'>in</span> (<span class='ident'>n</span> <span class='op'>/</span> <span class='number'>2</span> <span class='op'>+</span> <span class='number'>1</span>)..<span class='ident'>n</span> {
<span class='ident'>cdata</span>[<span class='ident'>i</span>] <span class='op'>=</span> <span class='ident'>cdata</span>[<span class='ident'>n</span> <span class='op'>-</span> <span class='ident'>i</span>].<span class='ident'>conj</span>();
}
<span class='ident'>cdata</span>
}
<span class='kw'>fn</span> <span class='ident'>compose</span>(<span class='ident'>data</span>: <span class='kw-2'>&amp;</span><span class='kw-2'>mut</span> [<span class='ident'>c64</span>], <span class='ident'>n</span>: <span class='ident'>usize</span>, <span class='ident'>inverse</span>: <span class='ident'>bool</span>) {
<span class='ident'>data</span>[<span class='number'>0</span>] <span class='op'>=</span> <span class='ident'>c64</span>(<span class='ident'>data</span>[<span class='number'>0</span>].<span class='ident'>re</span>() <span class='op'>+</span> <span class='ident'>data</span>[<span class='number'>0</span>].<span class='ident'>im</span>(), <span class='ident'>data</span>[<span class='number'>0</span>].<span class='ident'>re</span>() <span class='op'>-</span> <span class='ident'>data</span>[<span class='number'>0</span>].<span class='ident'>im</span>());
<span class='kw'>if</span> <span class='ident'>inverse</span> {
<span class='ident'>data</span>[<span class='number'>0</span>] <span class='op'>=</span> <span class='ident'>data</span>[<span class='number'>0</span>] <span class='op'>*</span> <span class='number'>0.5</span>;
}
<span class='kw'>let</span> <span class='ident'>sign</span> <span class='op'>=</span> <span class='kw'>if</span> <span class='ident'>inverse</span> { <span class='number'>1.0</span> } <span class='kw'>else</span> { <span class='op'>-</span><span class='number'>1.0</span> };
<span class='kw'>let</span> (<span class='ident'>multiplier</span>, <span class='kw-2'>mut</span> <span class='ident'>factor</span>) <span class='op'>=</span> {
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span>;
<span class='kw'>let</span> <span class='ident'>theta</span> <span class='op'>=</span> <span class='ident'>sign</span> <span class='op'>*</span> <span class='ident'>PI</span> <span class='op'>/</span> <span class='ident'>n</span> <span class='kw'>as</span> <span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>sine</span> <span class='op'>=</span> (<span class='number'>0.5</span> <span class='op'>*</span> <span class='ident'>theta</span>).<span class='ident'>sin</span>();
(<span class='ident'>c64</span>(<span class='op'>-</span><span class='number'>2.0</span> <span class='op'>*</span> <span class='ident'>sine</span> <span class='op'>*</span> <span class='ident'>sine</span>, <span class='ident'>theta</span>.<span class='ident'>sin</span>()), <span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='number'>0.0</span>))
};
<span class='kw'>for</span> <span class='ident'>i</span> <span class='kw'>in</span> <span class='number'>1</span>..(<span class='ident'>n</span> <span class='op'>/</span> <span class='number'>2</span>) {
<span class='kw'>let</span> <span class='ident'>j</span> <span class='op'>=</span> <span class='ident'>n</span> <span class='op'>-</span> <span class='ident'>i</span>;
<span class='ident'>factor</span> <span class='op'>=</span> <span class='ident'>multiplier</span> <span class='op'>*</span> <span class='ident'>factor</span> <span class='op'>+</span> <span class='ident'>factor</span>;
<span class='kw'>let</span> <span class='ident'>part1</span> <span class='op'>=</span> (<span class='ident'>data</span>[<span class='ident'>i</span>] <span class='op'>+</span> <span class='ident'>data</span>[<span class='ident'>j</span>].<span class='ident'>conj</span>()) <span class='op'>*</span> <span class='number'>0.5</span>;
<span class='kw'>let</span> <span class='ident'>part2</span> <span class='op'>=</span> (<span class='ident'>data</span>[<span class='ident'>i</span>] <span class='op'>-</span> <span class='ident'>data</span>[<span class='ident'>j</span>].<span class='ident'>conj</span>()) <span class='op'>*</span> <span class='number'>0.5</span>;
<span class='kw'>let</span> <span class='ident'>product</span> <span class='op'>=</span> <span class='ident'>c64</span>(<span class='number'>0.0</span>, <span class='ident'>sign</span>) <span class='op'>*</span> <span class='ident'>factor</span> <span class='op'>*</span> <span class='ident'>part2</span>;
<span class='ident'>data</span>[<span class='ident'>i</span>] <span class='op'>=</span> <span class='ident'>part1</span> <span class='op'>+</span> <span class='ident'>product</span>;
<span class='ident'>data</span>[<span class='ident'>j</span>] <span class='op'>=</span> (<span class='ident'>part1</span> <span class='op'>-</span> <span class='ident'>product</span>).<span class='ident'>conj</span>();
}
<span class='ident'>data</span>[<span class='ident'>n</span> <span class='op'>/</span> <span class='number'>2</span>] <span class='op'>=</span> <span class='ident'>data</span>[<span class='ident'>n</span> <span class='op'>/</span> <span class='number'>2</span>].<span class='ident'>conj</span>();
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>test</span>)]</span>
<span class='kw'>mod</span> <span class='ident'>tests</span> {
<span class='kw'>use</span> <span class='ident'>number</span>::<span class='ident'>c64</span>;
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>unpack</span>() {
<span class='kw'>let</span> <span class='ident'>data</span> <span class='op'>=</span> (<span class='number'>0</span>..<span class='number'>4</span>).<span class='ident'>map</span>(<span class='op'>|</span><span class='ident'>i</span><span class='op'>|</span> (<span class='ident'>i</span> <span class='op'>+</span> <span class='number'>1</span>) <span class='kw'>as</span> <span class='ident'>f64</span>).<span class='ident'>collect</span>::<span class='op'>&lt;</span><span class='ident'>Vec</span><span class='op'>&lt;</span>_<span class='op'>&gt;&gt;</span>();
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>super</span>::<span class='ident'>unpack</span>(<span class='kw-2'>&amp;</span><span class='ident'>data</span>), <span class='macro'>vec</span><span class='macro'>!</span>[
<span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='number'>0.0</span>), <span class='ident'>c64</span>(<span class='number'>3.0</span>, <span class='number'>4.0</span>), <span class='ident'>c64</span>(<span class='number'>2.0</span>, <span class='number'>0.0</span>), <span class='ident'>c64</span>(<span class='number'>3.0</span>, <span class='op'>-</span><span class='number'>4.0</span>),
]);
<span class='kw'>let</span> <span class='ident'>data</span> <span class='op'>=</span> (<span class='number'>0</span>..<span class='number'>8</span>).<span class='ident'>map</span>(<span class='op'>|</span><span class='ident'>i</span><span class='op'>|</span> (<span class='ident'>i</span> <span class='op'>+</span> <span class='number'>1</span>) <span class='kw'>as</span> <span class='ident'>f64</span>).<span class='ident'>collect</span>::<span class='op'>&lt;</span><span class='ident'>Vec</span><span class='op'>&lt;</span>_<span class='op'>&gt;&gt;</span>();
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>super</span>::<span class='ident'>unpack</span>(<span class='kw-2'>&amp;</span><span class='ident'>data</span>), <span class='macro'>vec</span><span class='macro'>!</span>[
<span class='ident'>c64</span>(<span class='number'>1.0</span>, <span class='number'>0.0</span>), <span class='ident'>c64</span>(<span class='number'>3.0</span>, <span class='number'>4.0</span>), <span class='ident'>c64</span>(<span class='number'>5.0</span>, <span class='number'>6.0</span>), <span class='ident'>c64</span>(<span class='number'>7.0</span>, <span class='number'>8.0</span>),
<span class='ident'>c64</span>(<span class='number'>2.0</span>, <span class='number'>0.0</span>), <span class='ident'>c64</span>(<span class='number'>7.0</span>, <span class='op'>-</span><span class='number'>8.0</span>), <span class='ident'>c64</span>(<span class='number'>5.0</span>, <span class='op'>-</span><span class='number'>6.0</span>), <span class='ident'>c64</span>(<span class='number'>3.0</span>, <span class='op'>-</span><span class='number'>4.0</span>),
]);
}
}
</pre>
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