| <!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="A trait for real number types that do not necessarily have floating-point-specific characteristics such as NaN and infinity."><meta name="keywords" content="rust, rustlang, rust-lang, Real"><title>Real in num_traits::real - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" 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class="sidebar-menu-toggle">☰</button><a class="sidebar-logo" href="../../num_traits/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><h2></h2></nav><nav class="sidebar"><a class="sidebar-logo" href="../../num_traits/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><h2 class="location"><a href="#">Real</a></h2><div class="sidebar-elems"><section><h3><a href="#required-methods">Required Methods</a></h3><ul class="block"><li><a href="#tymethod.abs">abs</a></li><li><a href="#tymethod.abs_sub">abs_sub</a></li><li><a href="#tymethod.acos">acos</a></li><li><a href="#tymethod.acosh">acosh</a></li><li><a href="#tymethod.asin">asin</a></li><li><a href="#tymethod.asinh">asinh</a></li><li><a href="#tymethod.atan">atan</a></li><li><a href="#tymethod.atan2">atan2</a></li><li><a href="#tymethod.atanh">atanh</a></li><li><a href="#tymethod.cbrt">cbrt</a></li><li><a href="#tymethod.ceil">ceil</a></li><li><a href="#tymethod.cos">cos</a></li><li><a href="#tymethod.cosh">cosh</a></li><li><a href="#tymethod.epsilon">epsilon</a></li><li><a href="#tymethod.exp">exp</a></li><li><a href="#tymethod.exp2">exp2</a></li><li><a href="#tymethod.exp_m1">exp_m1</a></li><li><a href="#tymethod.floor">floor</a></li><li><a href="#tymethod.fract">fract</a></li><li><a href="#tymethod.hypot">hypot</a></li><li><a href="#tymethod.is_sign_negative">is_sign_negative</a></li><li><a href="#tymethod.is_sign_positive">is_sign_positive</a></li><li><a href="#tymethod.ln">ln</a></li><li><a href="#tymethod.ln_1p">ln_1p</a></li><li><a href="#tymethod.log">log</a></li><li><a href="#tymethod.log10">log10</a></li><li><a href="#tymethod.log2">log2</a></li><li><a href="#tymethod.max">max</a></li><li><a href="#tymethod.max_value">max_value</a></li><li><a href="#tymethod.min">min</a></li><li><a href="#tymethod.min_positive_value">min_positive_value</a></li><li><a href="#tymethod.min_value">min_value</a></li><li><a href="#tymethod.mul_add">mul_add</a></li><li><a href="#tymethod.powf">powf</a></li><li><a href="#tymethod.powi">powi</a></li><li><a href="#tymethod.recip">recip</a></li><li><a href="#tymethod.round">round</a></li><li><a href="#tymethod.signum">signum</a></li><li><a href="#tymethod.sin">sin</a></li><li><a href="#tymethod.sin_cos">sin_cos</a></li><li><a href="#tymethod.sinh">sinh</a></li><li><a href="#tymethod.sqrt">sqrt</a></li><li><a href="#tymethod.tan">tan</a></li><li><a href="#tymethod.tanh">tanh</a></li><li><a href="#tymethod.to_degrees">to_degrees</a></li><li><a href="#tymethod.to_radians">to_radians</a></li><li><a href="#tymethod.trunc">trunc</a></li></ul><h3><a href="#implementors">Implementors</a></h3></section><h2><a href="index.html">In num_traits::real</a></h2></div></nav><main><div class="width-limiter"><nav class="sub"><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1 class="fqn">Trait <a href="../index.html">num_traits</a>::<wbr><a href="index.html">real</a>::<wbr><a class="trait" href="#">Real</a><button id="copy-path" onclick="copy_path(this)" title="Copy item path to clipboard"><img src="../../clipboard.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="srclink" href="../../src/num_traits/real.rs.html#17-780">source</a> · <a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class="inner">−</span>]</a></span></div><div class="item-decl"><pre class="rust trait"><code>pub trait Real: <a class="trait" href="../trait.Num.html" title="trait num_traits::Num">Num</a> + Copy + <a class="trait" href="../cast/trait.NumCast.html" title="trait num_traits::cast::NumCast">NumCast</a> + PartialOrd + Neg<Output = Self> { |
| <details class="rustdoc-toggle type-contents-toggle"><summary class="hideme"><span>Show 47 methods</span></summary> fn <a href="#tymethod.min_value" class="fnname">min_value</a>() -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.min_positive_value" class="fnname">min_positive_value</a>() -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.epsilon" class="fnname">epsilon</a>() -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.max_value" class="fnname">max_value</a>() -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.floor" class="fnname">floor</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.ceil" class="fnname">ceil</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.round" class="fnname">round</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.trunc" class="fnname">trunc</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.fract" class="fnname">fract</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.abs" class="fnname">abs</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.signum" class="fnname">signum</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.is_sign_positive" class="fnname">is_sign_positive</a>(self) -> bool; |
| <span class="item-spacer"></span> fn <a href="#tymethod.is_sign_negative" class="fnname">is_sign_negative</a>(self) -> bool; |
| <span class="item-spacer"></span> fn <a href="#tymethod.mul_add" class="fnname">mul_add</a>(self, a: Self, b: Self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.recip" class="fnname">recip</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.powi" class="fnname">powi</a>(self, n: i32) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.powf" class="fnname">powf</a>(self, n: Self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.sqrt" class="fnname">sqrt</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.exp" class="fnname">exp</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.exp2" class="fnname">exp2</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.ln" class="fnname">ln</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.log" class="fnname">log</a>(self, base: Self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.log2" class="fnname">log2</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.log10" class="fnname">log10</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.to_degrees" class="fnname">to_degrees</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.to_radians" class="fnname">to_radians</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.max" class="fnname">max</a>(self, other: Self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.min" class="fnname">min</a>(self, other: Self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.abs_sub" class="fnname">abs_sub</a>(self, other: Self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.cbrt" class="fnname">cbrt</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.hypot" class="fnname">hypot</a>(self, other: Self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.sin" class="fnname">sin</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.cos" class="fnname">cos</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.tan" class="fnname">tan</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.asin" class="fnname">asin</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.acos" class="fnname">acos</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.atan" class="fnname">atan</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.atan2" class="fnname">atan2</a>(self, other: Self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.sin_cos" class="fnname">sin_cos</a>(self) -> (Self, Self); |
| <span class="item-spacer"></span> fn <a href="#tymethod.exp_m1" class="fnname">exp_m1</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.ln_1p" class="fnname">ln_1p</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.sinh" class="fnname">sinh</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.cosh" class="fnname">cosh</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.tanh" class="fnname">tanh</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.asinh" class="fnname">asinh</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.acosh" class="fnname">acosh</a>(self) -> Self; |
| <span class="item-spacer"></span> fn <a href="#tymethod.atanh" class="fnname">atanh</a>(self) -> Self; |
| </details>}</code></pre></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>A trait for real number types that do not necessarily have |
| floating-point-specific characteristics such as NaN and infinity.</p> |
| <p>See <a href="https://en.wikipedia.org/wiki/Real_data_type">this Wikipedia article</a> |
| for a list of data types that could meaningfully implement this trait.</p> |
| <p>This trait is only available with the <code>std</code> feature, or with the <code>libm</code> feature otherwise.</p> |
| </div></details><h2 id="required-methods" class="small-section-header">Required Methods<a href="#required-methods" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.min_value" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#28">source</a><h4 class="code-header">fn <a href="#tymethod.min_value" class="fnname">min_value</a>() -> Self</h4></section></summary><div class="docblock"><p>Returns the smallest finite value that this type can represent.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>x: f64 = Real::min_value(); |
| |
| <span class="macro">assert_eq!</span>(x, f64::MIN);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.min_positive_value" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#40">source</a><h4 class="code-header">fn <a href="#tymethod.min_positive_value" class="fnname">min_positive_value</a>() -> Self</h4></section></summary><div class="docblock"><p>Returns the smallest positive, normalized value that this type can represent.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>x: f64 = Real::min_positive_value(); |
| |
| <span class="macro">assert_eq!</span>(x, f64::MIN_POSITIVE);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.epsilon" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#57">source</a><h4 class="code-header">fn <a href="#tymethod.epsilon" class="fnname">epsilon</a>() -> Self</h4></section></summary><div class="docblock"><p>Returns epsilon, a small positive value.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>x: f64 = Real::epsilon(); |
| |
| <span class="macro">assert_eq!</span>(x, f64::EPSILON);</code></pre></div> |
| <h5 id="panics"><a href="#panics">Panics</a></h5> |
| <p>The default implementation will panic if <code>f32::EPSILON</code> cannot |
| be cast to <code>Self</code>.</p> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.max_value" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#68">source</a><h4 class="code-header">fn <a href="#tymethod.max_value" class="fnname">max_value</a>() -> Self</h4></section></summary><div class="docblock"><p>Returns the largest finite value that this type can represent.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>x: f64 = Real::max_value(); |
| <span class="macro">assert_eq!</span>(x, f64::MAX);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.floor" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#81">source</a><h4 class="code-header">fn <a href="#tymethod.floor" class="fnname">floor</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the largest integer less than or equal to a number.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>f = <span class="number">3.99</span>; |
| <span class="kw">let </span>g = <span class="number">3.0</span>; |
| |
| <span class="macro">assert_eq!</span>(f.floor(), <span class="number">3.0</span>); |
| <span class="macro">assert_eq!</span>(g.floor(), <span class="number">3.0</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.ceil" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#94">source</a><h4 class="code-header">fn <a href="#tymethod.ceil" class="fnname">ceil</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the smallest integer greater than or equal to a number.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>f = <span class="number">3.01</span>; |
| <span class="kw">let </span>g = <span class="number">4.0</span>; |
| |
| <span class="macro">assert_eq!</span>(f.ceil(), <span class="number">4.0</span>); |
| <span class="macro">assert_eq!</span>(g.ceil(), <span class="number">4.0</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.round" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#108">source</a><h4 class="code-header">fn <a href="#tymethod.round" class="fnname">round</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the nearest integer to a number. Round half-way cases away from |
| <code>0.0</code>.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>f = <span class="number">3.3</span>; |
| <span class="kw">let </span>g = -<span class="number">3.3</span>; |
| |
| <span class="macro">assert_eq!</span>(f.round(), <span class="number">3.0</span>); |
| <span class="macro">assert_eq!</span>(g.round(), -<span class="number">3.0</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.trunc" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#121">source</a><h4 class="code-header">fn <a href="#tymethod.trunc" class="fnname">trunc</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Return the integer part of a number.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>f = <span class="number">3.3</span>; |
| <span class="kw">let </span>g = -<span class="number">3.7</span>; |
| |
| <span class="macro">assert_eq!</span>(f.trunc(), <span class="number">3.0</span>); |
| <span class="macro">assert_eq!</span>(g.trunc(), -<span class="number">3.0</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.fract" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#136">source</a><h4 class="code-header">fn <a href="#tymethod.fract" class="fnname">fract</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the fractional part of a number.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">3.5</span>; |
| <span class="kw">let </span>y = -<span class="number">3.5</span>; |
| <span class="kw">let </span>abs_difference_x = (x.fract() - <span class="number">0.5</span>).abs(); |
| <span class="kw">let </span>abs_difference_y = (y.fract() - (-<span class="number">0.5</span>)).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference_x < <span class="number">1e-10</span>); |
| <span class="macro">assert!</span>(abs_difference_y < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.abs" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#156">source</a><h4 class="code-header">fn <a href="#tymethod.abs" class="fnname">abs</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Computes the absolute value of <code>self</code>. Returns <code>Float::nan()</code> if the |
| number is <code>Float::nan()</code>.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>x = <span class="number">3.5</span>; |
| <span class="kw">let </span>y = -<span class="number">3.5</span>; |
| |
| <span class="kw">let </span>abs_difference_x = (x.abs() - x).abs(); |
| <span class="kw">let </span>abs_difference_y = (y.abs() - (-y)).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference_x < <span class="number">1e-10</span>); |
| <span class="macro">assert!</span>(abs_difference_y < <span class="number">1e-10</span>); |
| |
| <span class="macro">assert!</span>(::num_traits::Float::is_nan(f64::NAN.abs()));</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.signum" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#175">source</a><h4 class="code-header">fn <a href="#tymethod.signum" class="fnname">signum</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns a number that represents the sign of <code>self</code>.</p> |
| <ul> |
| <li><code>1.0</code> if the number is positive, <code>+0.0</code> or <code>Float::infinity()</code></li> |
| <li><code>-1.0</code> if the number is negative, <code>-0.0</code> or <code>Float::neg_infinity()</code></li> |
| <li><code>Float::nan()</code> if the number is <code>Float::nan()</code></li> |
| </ul> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>f = <span class="number">3.5</span>; |
| |
| <span class="macro">assert_eq!</span>(f.signum(), <span class="number">1.0</span>); |
| <span class="macro">assert_eq!</span>(f64::NEG_INFINITY.signum(), -<span class="number">1.0</span>); |
| |
| <span class="macro">assert!</span>(f64::NAN.signum().is_nan());</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.is_sign_positive" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#193">source</a><h4 class="code-header">fn <a href="#tymethod.is_sign_positive" class="fnname">is_sign_positive</a>(self) -> bool</h4></section></summary><div class="docblock"><p>Returns <code>true</code> if <code>self</code> is positive, including <code>+0.0</code>, |
| <code>Float::infinity()</code>, and with newer versions of Rust <code>f64::NAN</code>.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>neg_nan: f64 = -f64::NAN; |
| |
| <span class="kw">let </span>f = <span class="number">7.0</span>; |
| <span class="kw">let </span>g = -<span class="number">7.0</span>; |
| |
| <span class="macro">assert!</span>(f.is_sign_positive()); |
| <span class="macro">assert!</span>(!g.is_sign_positive()); |
| <span class="macro">assert!</span>(!neg_nan.is_sign_positive());</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.is_sign_negative" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#211">source</a><h4 class="code-header">fn <a href="#tymethod.is_sign_negative" class="fnname">is_sign_negative</a>(self) -> bool</h4></section></summary><div class="docblock"><p>Returns <code>true</code> if <code>self</code> is negative, including <code>-0.0</code>, |
| <code>Float::neg_infinity()</code>, and with newer versions of Rust <code>-f64::NAN</code>.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>nan: f64 = f64::NAN; |
| |
| <span class="kw">let </span>f = <span class="number">7.0</span>; |
| <span class="kw">let </span>g = -<span class="number">7.0</span>; |
| |
| <span class="macro">assert!</span>(!f.is_sign_negative()); |
| <span class="macro">assert!</span>(g.is_sign_negative()); |
| <span class="macro">assert!</span>(!nan.is_sign_negative());</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.mul_add" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#231">source</a><h4 class="code-header">fn <a href="#tymethod.mul_add" class="fnname">mul_add</a>(self, a: Self, b: Self) -> Self</h4></section></summary><div class="docblock"><p>Fused multiply-add. Computes <code>(self * a) + b</code> with only one rounding |
| error, yielding a more accurate result than an unfused multiply-add.</p> |
| <p>Using <code>mul_add</code> can be more performant than an unfused multiply-add if |
| the target architecture has a dedicated <code>fma</code> CPU instruction.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>m = <span class="number">10.0</span>; |
| <span class="kw">let </span>x = <span class="number">4.0</span>; |
| <span class="kw">let </span>b = <span class="number">60.0</span>; |
| |
| <span class="comment">// 100.0 |
| </span><span class="kw">let </span>abs_difference = (m.mul_add(x, b) - (m<span class="kw-2">*</span>x + b)).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.recip" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#243">source</a><h4 class="code-header">fn <a href="#tymethod.recip" class="fnname">recip</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Take the reciprocal (inverse) of a number, <code>1/x</code>.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">2.0</span>; |
| <span class="kw">let </span>abs_difference = (x.recip() - (<span class="number">1.0</span>/x)).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.powi" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#257">source</a><h4 class="code-header">fn <a href="#tymethod.powi" class="fnname">powi</a>(self, n: i32) -> Self</h4></section></summary><div class="docblock"><p>Raise a number to an integer power.</p> |
| <p>Using this function is generally faster than using <code>powf</code></p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">2.0</span>; |
| <span class="kw">let </span>abs_difference = (x.powi(<span class="number">2</span>) - x<span class="kw-2">*</span>x).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.powf" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#269">source</a><h4 class="code-header">fn <a href="#tymethod.powf" class="fnname">powf</a>(self, n: Self) -> Self</h4></section></summary><div class="docblock"><p>Raise a number to a real number power.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">2.0</span>; |
| <span class="kw">let </span>abs_difference = (x.powf(<span class="number">2.0</span>) - x<span class="kw-2">*</span>x).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.sqrt" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#290">source</a><h4 class="code-header">fn <a href="#tymethod.sqrt" class="fnname">sqrt</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Take the square root of a number.</p> |
| <p>Returns NaN if <code>self</code> is a negative floating-point number.</p> |
| <h5 id="panics-1"><a href="#panics-1">Panics</a></h5> |
| <p>If the implementing type doesn’t support NaN, this method should panic if <code>self < 0</code>.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>positive = <span class="number">4.0</span>; |
| <span class="kw">let </span>negative = -<span class="number">4.0</span>; |
| |
| <span class="kw">let </span>abs_difference = (positive.sqrt() - <span class="number">2.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>); |
| <span class="macro">assert!</span>(::num_traits::Float::is_nan(negative.sqrt()));</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.exp" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#306">source</a><h4 class="code-header">fn <a href="#tymethod.exp" class="fnname">exp</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns <code>e^(self)</code>, (the exponential function).</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>one = <span class="number">1.0</span>; |
| <span class="comment">// e^1 |
| </span><span class="kw">let </span>e = one.exp(); |
| |
| <span class="comment">// ln(e) - 1 == 0 |
| </span><span class="kw">let </span>abs_difference = (e.ln() - <span class="number">1.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.exp2" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#320">source</a><h4 class="code-header">fn <a href="#tymethod.exp2" class="fnname">exp2</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns <code>2^(self)</code>.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>f = <span class="number">2.0</span>; |
| |
| <span class="comment">// 2^2 - 4 == 0 |
| </span><span class="kw">let </span>abs_difference = (f.exp2() - <span class="number">4.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.ln" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#340">source</a><h4 class="code-header">fn <a href="#tymethod.ln" class="fnname">ln</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the natural logarithm of the number.</p> |
| <h5 id="panics-2"><a href="#panics-2">Panics</a></h5> |
| <p>If <code>self <= 0</code> and this type does not support a NaN representation, this function should panic.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>one = <span class="number">1.0</span>; |
| <span class="comment">// e^1 |
| </span><span class="kw">let </span>e = one.exp(); |
| |
| <span class="comment">// ln(e) - 1 == 0 |
| </span><span class="kw">let </span>abs_difference = (e.ln() - <span class="number">1.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.log" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#363">source</a><h4 class="code-header">fn <a href="#tymethod.log" class="fnname">log</a>(self, base: Self) -> Self</h4></section></summary><div class="docblock"><p>Returns the logarithm of the number with respect to an arbitrary base.</p> |
| <h5 id="panics-3"><a href="#panics-3">Panics</a></h5> |
| <p>If <code>self <= 0</code> and this type does not support a NaN representation, this function should panic.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>ten = <span class="number">10.0</span>; |
| <span class="kw">let </span>two = <span class="number">2.0</span>; |
| |
| <span class="comment">// log10(10) - 1 == 0 |
| </span><span class="kw">let </span>abs_difference_10 = (ten.log(<span class="number">10.0</span>) - <span class="number">1.0</span>).abs(); |
| |
| <span class="comment">// log2(2) - 1 == 0 |
| </span><span class="kw">let </span>abs_difference_2 = (two.log(<span class="number">2.0</span>) - <span class="number">1.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference_10 < <span class="number">1e-10</span>); |
| <span class="macro">assert!</span>(abs_difference_2 < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.log2" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#381">source</a><h4 class="code-header">fn <a href="#tymethod.log2" class="fnname">log2</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the base 2 logarithm of the number.</p> |
| <h5 id="panics-4"><a href="#panics-4">Panics</a></h5> |
| <p>If <code>self <= 0</code> and this type does not support a NaN representation, this function should panic.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>two = <span class="number">2.0</span>; |
| |
| <span class="comment">// log2(2) - 1 == 0 |
| </span><span class="kw">let </span>abs_difference = (two.log2() - <span class="number">1.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.log10" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#400">source</a><h4 class="code-header">fn <a href="#tymethod.log10" class="fnname">log10</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the base 10 logarithm of the number.</p> |
| <h5 id="panics-5"><a href="#panics-5">Panics</a></h5> |
| <p>If <code>self <= 0</code> and this type does not support a NaN representation, this function should panic.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>ten = <span class="number">10.0</span>; |
| |
| <span class="comment">// log10(10) - 1 == 0 |
| </span><span class="kw">let </span>abs_difference = (ten.log10() - <span class="number">1.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.to_degrees" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#413">source</a><h4 class="code-header">fn <a href="#tymethod.to_degrees" class="fnname">to_degrees</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Converts radians to degrees.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>std::f64::consts; |
| |
| <span class="kw">let </span>angle = consts::PI; |
| |
| <span class="kw">let </span>abs_difference = (angle.to_degrees() - <span class="number">180.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.to_radians" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#426">source</a><h4 class="code-header">fn <a href="#tymethod.to_radians" class="fnname">to_radians</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Converts degrees to radians.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>std::f64::consts; |
| |
| <span class="kw">let </span>angle = <span class="number">180.0_f64</span>; |
| |
| <span class="kw">let </span>abs_difference = (angle.to_radians() - consts::PI).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.max" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#438">source</a><h4 class="code-header">fn <a href="#tymethod.max" class="fnname">max</a>(self, other: Self) -> Self</h4></section></summary><div class="docblock"><p>Returns the maximum of the two numbers.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">1.0</span>; |
| <span class="kw">let </span>y = <span class="number">2.0</span>; |
| |
| <span class="macro">assert_eq!</span>(x.max(y), y);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.min" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#450">source</a><h4 class="code-header">fn <a href="#tymethod.min" class="fnname">min</a>(self, other: Self) -> Self</h4></section></summary><div class="docblock"><p>Returns the minimum of the two numbers.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">1.0</span>; |
| <span class="kw">let </span>y = <span class="number">2.0</span>; |
| |
| <span class="macro">assert_eq!</span>(x.min(y), x);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.abs_sub" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#469">source</a><h4 class="code-header">fn <a href="#tymethod.abs_sub" class="fnname">abs_sub</a>(self, other: Self) -> Self</h4></section></summary><div class="docblock"><p>The positive difference of two numbers.</p> |
| <ul> |
| <li>If <code>self <= other</code>: <code>0:0</code></li> |
| <li>Else: <code>self - other</code></li> |
| </ul> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">3.0</span>; |
| <span class="kw">let </span>y = -<span class="number">3.0</span>; |
| |
| <span class="kw">let </span>abs_difference_x = (x.abs_sub(<span class="number">1.0</span>) - <span class="number">2.0</span>).abs(); |
| <span class="kw">let </span>abs_difference_y = (y.abs_sub(<span class="number">1.0</span>) - <span class="number">0.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference_x < <span class="number">1e-10</span>); |
| <span class="macro">assert!</span>(abs_difference_y < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.cbrt" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#483">source</a><h4 class="code-header">fn <a href="#tymethod.cbrt" class="fnname">cbrt</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Take the cubic root of a number.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">8.0</span>; |
| |
| <span class="comment">// x^(1/3) - 2 == 0 |
| </span><span class="kw">let </span>abs_difference = (x.cbrt() - <span class="number">2.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.hypot" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#499">source</a><h4 class="code-header">fn <a href="#tymethod.hypot" class="fnname">hypot</a>(self, other: Self) -> Self</h4></section></summary><div class="docblock"><p>Calculate the length of the hypotenuse of a right-angle triangle given |
| legs of length <code>x</code> and <code>y</code>.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">2.0</span>; |
| <span class="kw">let </span>y = <span class="number">3.0</span>; |
| |
| <span class="comment">// sqrt(x^2 + y^2) |
| </span><span class="kw">let </span>abs_difference = (x.hypot(y) - (x.powi(<span class="number">2</span>) + y.powi(<span class="number">2</span>)).sqrt()).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.sin" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#513">source</a><h4 class="code-header">fn <a href="#tymethod.sin" class="fnname">sin</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Computes the sine of a number (in radians).</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>x = f64::consts::PI/<span class="number">2.0</span>; |
| |
| <span class="kw">let </span>abs_difference = (x.sin() - <span class="number">1.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.cos" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#527">source</a><h4 class="code-header">fn <a href="#tymethod.cos" class="fnname">cos</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Computes the cosine of a number (in radians).</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>x = <span class="number">2.0</span><span class="kw-2">*</span>f64::consts::PI; |
| |
| <span class="kw">let </span>abs_difference = (x.cos() - <span class="number">1.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.tan" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#540">source</a><h4 class="code-header">fn <a href="#tymethod.tan" class="fnname">tan</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Computes the tangent of a number (in radians).</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>x = f64::consts::PI/<span class="number">4.0</span>; |
| <span class="kw">let </span>abs_difference = (x.tan() - <span class="number">1.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-14</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.asin" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#562">source</a><h4 class="code-header">fn <a href="#tymethod.asin" class="fnname">asin</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Computes the arcsine of a number. Return value is in radians in |
| the range [-pi/2, pi/2] or NaN if the number is outside the range |
| [-1, 1].</p> |
| <h5 id="panics-6"><a href="#panics-6">Panics</a></h5> |
| <p>If this type does not support a NaN representation, this function should panic |
| if the number is outside the range [-1, 1].</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>f = f64::consts::PI / <span class="number">2.0</span>; |
| |
| <span class="comment">// asin(sin(pi/2)) |
| </span><span class="kw">let </span>abs_difference = (f.sin().asin() - f64::consts::PI / <span class="number">2.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.acos" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#584">source</a><h4 class="code-header">fn <a href="#tymethod.acos" class="fnname">acos</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Computes the arccosine of a number. Return value is in radians in |
| the range [0, pi] or NaN if the number is outside the range |
| [-1, 1].</p> |
| <h5 id="panics-7"><a href="#panics-7">Panics</a></h5> |
| <p>If this type does not support a NaN representation, this function should panic |
| if the number is outside the range [-1, 1].</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>f = f64::consts::PI / <span class="number">4.0</span>; |
| |
| <span class="comment">// acos(cos(pi/4)) |
| </span><span class="kw">let </span>abs_difference = (f.cos().acos() - f64::consts::PI / <span class="number">4.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.atan" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#599">source</a><h4 class="code-header">fn <a href="#tymethod.atan" class="fnname">atan</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Computes the arctangent of a number. Return value is in radians in the |
| range [-pi/2, pi/2];</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>f = <span class="number">1.0</span>; |
| |
| <span class="comment">// atan(tan(1)) |
| </span><span class="kw">let </span>abs_difference = (f.tan().atan() - <span class="number">1.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.atan2" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#628">source</a><h4 class="code-header">fn <a href="#tymethod.atan2" class="fnname">atan2</a>(self, other: Self) -> Self</h4></section></summary><div class="docblock"><p>Computes the four quadrant arctangent of <code>self</code> (<code>y</code>) and <code>other</code> (<code>x</code>).</p> |
| <ul> |
| <li><code>x = 0</code>, <code>y = 0</code>: <code>0</code></li> |
| <li><code>x >= 0</code>: <code>arctan(y/x)</code> -> <code>[-pi/2, pi/2]</code></li> |
| <li><code>y >= 0</code>: <code>arctan(y/x) + pi</code> -> <code>(pi/2, pi]</code></li> |
| <li><code>y < 0</code>: <code>arctan(y/x) - pi</code> -> <code>(-pi, -pi/2)</code></li> |
| </ul> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>pi = f64::consts::PI; |
| <span class="comment">// All angles from horizontal right (+x) |
| // 45 deg counter-clockwise |
| </span><span class="kw">let </span>x1 = <span class="number">3.0</span>; |
| <span class="kw">let </span>y1 = -<span class="number">3.0</span>; |
| |
| <span class="comment">// 135 deg clockwise |
| </span><span class="kw">let </span>x2 = -<span class="number">3.0</span>; |
| <span class="kw">let </span>y2 = <span class="number">3.0</span>; |
| |
| <span class="kw">let </span>abs_difference_1 = (y1.atan2(x1) - (-pi/<span class="number">4.0</span>)).abs(); |
| <span class="kw">let </span>abs_difference_2 = (y2.atan2(x2) - <span class="number">3.0</span><span class="kw-2">*</span>pi/<span class="number">4.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference_1 < <span class="number">1e-10</span>); |
| <span class="macro">assert!</span>(abs_difference_2 < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.sin_cos" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#646">source</a><h4 class="code-header">fn <a href="#tymethod.sin_cos" class="fnname">sin_cos</a>(self) -> (Self, Self)</h4></section></summary><div class="docblock"><p>Simultaneously computes the sine and cosine of the number, <code>x</code>. Returns |
| <code>(sin(x), cos(x))</code>.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>x = f64::consts::PI/<span class="number">4.0</span>; |
| <span class="kw">let </span>f = x.sin_cos(); |
| |
| <span class="kw">let </span>abs_difference_0 = (f.<span class="number">0 </span>- x.sin()).abs(); |
| <span class="kw">let </span>abs_difference_1 = (f.<span class="number">1 </span>- x.cos()).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference_0 < <span class="number">1e-10</span>); |
| <span class="macro">assert!</span>(abs_difference_0 < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.exp_m1" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#661">source</a><h4 class="code-header">fn <a href="#tymethod.exp_m1" class="fnname">exp_m1</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns <code>e^(self) - 1</code> in a way that is accurate even if the |
| number is close to zero.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">7.0</span>; |
| |
| <span class="comment">// e^(ln(7)) - 1 |
| </span><span class="kw">let </span>abs_difference = (x.ln().exp_m1() - <span class="number">6.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.ln_1p" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#682">source</a><h4 class="code-header">fn <a href="#tymethod.ln_1p" class="fnname">ln_1p</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns <code>ln(1+n)</code> (natural logarithm) more accurately than if |
| the operations were performed separately.</p> |
| <h5 id="panics-8"><a href="#panics-8">Panics</a></h5> |
| <p>If this type does not support a NaN representation, this function should panic |
| if <code>self-1 <= 0</code>.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>x = f64::consts::E - <span class="number">1.0</span>; |
| |
| <span class="comment">// ln(1 + (e - 1)) == ln(e) == 1 |
| </span><span class="kw">let </span>abs_difference = (x.ln_1p() - <span class="number">1.0</span>).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.sinh" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#700">source</a><h4 class="code-header">fn <a href="#tymethod.sinh" class="fnname">sinh</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Hyperbolic sine function.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>e = f64::consts::E; |
| <span class="kw">let </span>x = <span class="number">1.0</span>; |
| |
| <span class="kw">let </span>f = x.sinh(); |
| <span class="comment">// Solving sinh() at 1 gives `(e^2-1)/(2e)` |
| </span><span class="kw">let </span>g = (e<span class="kw-2">*</span>e - <span class="number">1.0</span>)/(<span class="number">2.0</span><span class="kw-2">*</span>e); |
| <span class="kw">let </span>abs_difference = (f - g).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.cosh" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#718">source</a><h4 class="code-header">fn <a href="#tymethod.cosh" class="fnname">cosh</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Hyperbolic cosine function.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>e = f64::consts::E; |
| <span class="kw">let </span>x = <span class="number">1.0</span>; |
| <span class="kw">let </span>f = x.cosh(); |
| <span class="comment">// Solving cosh() at 1 gives this result |
| </span><span class="kw">let </span>g = (e<span class="kw-2">*</span>e + <span class="number">1.0</span>)/(<span class="number">2.0</span><span class="kw-2">*</span>e); |
| <span class="kw">let </span>abs_difference = (f - g).abs(); |
| |
| <span class="comment">// Same result |
| </span><span class="macro">assert!</span>(abs_difference < <span class="number">1.0e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.tanh" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#736">source</a><h4 class="code-header">fn <a href="#tymethod.tanh" class="fnname">tanh</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Hyperbolic tangent function.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>e = f64::consts::E; |
| <span class="kw">let </span>x = <span class="number">1.0</span>; |
| |
| <span class="kw">let </span>f = x.tanh(); |
| <span class="comment">// Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))` |
| </span><span class="kw">let </span>g = (<span class="number">1.0 </span>- e.powi(-<span class="number">2</span>))/(<span class="number">1.0 </span>+ e.powi(-<span class="number">2</span>)); |
| <span class="kw">let </span>abs_difference = (f - g).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1.0e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.asinh" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#750">source</a><h4 class="code-header">fn <a href="#tymethod.asinh" class="fnname">asinh</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Inverse hyperbolic sine function.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">1.0</span>; |
| <span class="kw">let </span>f = x.sinh().asinh(); |
| |
| <span class="kw">let </span>abs_difference = (f - x).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1.0e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.acosh" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#764">source</a><h4 class="code-header">fn <a href="#tymethod.acosh" class="fnname">acosh</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Inverse hyperbolic cosine function.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| |
| <span class="kw">let </span>x = <span class="number">1.0</span>; |
| <span class="kw">let </span>f = x.cosh().acosh(); |
| |
| <span class="kw">let </span>abs_difference = (f - x).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1.0e-10</span>);</code></pre></div> |
| </div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.atanh" class="method has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#779">source</a><h4 class="code-header">fn <a href="#tymethod.atanh" class="fnname">atanh</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Inverse hyperbolic tangent function.</p> |
| |
| <div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real; |
| <span class="kw">use </span>std::f64; |
| |
| <span class="kw">let </span>e = f64::consts::E; |
| <span class="kw">let </span>f = e.tanh().atanh(); |
| |
| <span class="kw">let </span>abs_difference = (f - e).abs(); |
| |
| <span class="macro">assert!</span>(abs_difference < <span class="number">1.0e-10</span>);</code></pre></div> |
| </div></details></div><h2 id="implementors" class="small-section-header">Implementors<a href="#implementors" class="anchor"></a></h2><div id="implementors-list"><section id="impl-Real-for-T" class="impl has-srclink"><a class="srclink rightside" href="../../src/num_traits/real.rs.html#782-834">source</a><a href="#impl-Real-for-T" class="anchor"></a><h3 class="code-header">impl<T: <a class="trait" href="../float/trait.Float.html" title="trait num_traits::float::Float">Float</a>> <a class="trait" href="trait.Real.html" title="trait num_traits::real::Real">Real</a> for T</h3></section></div><script src="../../implementors/num_traits/real/trait.Real.js" async></script></section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="num_traits" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
