569 lines
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569 lines
59 KiB
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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="A trait for real number types that do not necessarily have floating-point-specific characteristics such as NaN and infinity."><title>Real in num_traits::real - Rust</title><script>if(window.location.protocol!=="file:")document.head.insertAdjacentHTML("beforeend","SourceSerif4-Regular-6b053e98.ttf.woff2,FiraSans-Italic-81dc35de.woff2,FiraSans-Regular-0fe48ade.woff2,FiraSans-MediumItalic-ccf7e434.woff2,FiraSans-Medium-e1aa3f0a.woff2,SourceCodePro-Regular-8badfe75.ttf.woff2,SourceCodePro-Semibold-aa29a496.ttf.woff2".split(",").map(f=>`<link rel="preload" as="font" type="font/woff2"href="../../static.files/${f}">`).join(""))</script><link rel="stylesheet" href="../../static.files/normalize-9960930a.css"><link rel="stylesheet" href="../../static.files/rustdoc-ca0dd0c4.css"><meta name="rustdoc-vars" data-root-path="../../" data-static-root-path="../../static.files/" data-current-crate="num_traits" data-themes="" data-resource-suffix="" data-rustdoc-version="1.93.1 (01f6ddf75 2026-02-11) (Arch Linux rust 1:1.93.1-1)" data-channel="1.93.1" data-search-js="search-9e2438ea.js" data-stringdex-js="stringdex-a3946164.js" data-settings-js="settings-c38705f0.js" ><script src="../../static.files/storage-e2aeef58.js"></script><script defer src="sidebar-items.js"></script><script defer src="../../static.files/main-a410ff4d.js"></script><noscript><link rel="stylesheet" href="../../static.files/noscript-263c88ec.css"></noscript><link rel="alternate icon" type="image/png" href="../../static.files/favicon-32x32-eab170b8.png"><link rel="icon" type="image/svg+xml" href="../../static.files/favicon-044be391.svg"></head><body class="rustdoc trait"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><rustdoc-topbar><h2><a href="#">Real</a></h2></rustdoc-topbar><nav class="sidebar"><div class="sidebar-crate"><h2><a href="../../num_traits/index.html">num_<wbr>traits</a><span class="version">0.2.19</span></h2></div><div class="sidebar-elems"><section id="rustdoc-toc"><h2 class="location"><a href="#">Real</a></h2><h3><a href="#required-methods">Required Methods</a></h3><ul class="block"><li><a href="#tymethod.abs" title="abs">abs</a></li><li><a href="#tymethod.abs_sub" title="abs_sub">abs_sub</a></li><li><a href="#tymethod.acos" title="acos">acos</a></li><li><a href="#tymethod.acosh" title="acosh">acosh</a></li><li><a href="#tymethod.asin" title="asin">asin</a></li><li><a href="#tymethod.asinh" title="asinh">asinh</a></li><li><a href="#tymethod.atan" title="atan">atan</a></li><li><a href="#tymethod.atan2" title="atan2">atan2</a></li><li><a href="#tymethod.atanh" title="atanh">atanh</a></li><li><a href="#tymethod.cbrt" title="cbrt">cbrt</a></li><li><a href="#tymethod.ceil" title="ceil">ceil</a></li><li><a href="#tymethod.cos" title="cos">cos</a></li><li><a href="#tymethod.cosh" title="cosh">cosh</a></li><li><a href="#tymethod.epsilon" title="epsilon">epsilon</a></li><li><a href="#tymethod.exp" title="exp">exp</a></li><li><a href="#tymethod.exp2" title="exp2">exp2</a></li><li><a href="#tymethod.exp_m1" title="exp_m1">exp_m1</a></li><li><a href="#tymethod.floor" title="floor">floor</a></li><li><a href="#tymethod.fract" title="fract">fract</a></li><li><a href="#tymethod.hypot" title="hypot">hypot</a></li><li><a href="#tymethod.is_sign_negative" title="is_sign_negative">is_sign_negative</a></li><li><a href="#tymethod.is_sign_positive" title="is_sign_positive">is_sign_positive</a></li><li><a href="#tymethod.ln" title="ln">ln</a></li><li><a href="#tymethod.ln_1p" title="ln_1p">ln_1p</a></li><li><a href="#tymethod.log" title="log">log</a></li><li><a href="#tymethod.log2" title="log2">log2</a></li><li><a href="#tymethod.log10" title="log10">log10</a></li><li><a href="#tymethod.max" title="max">max</a></li><li><a href="#tymethod.max_value" title="max_value">max_value</a></li><li><a href="#tymethod.min" title="min">min</a></li><li><a href="#tymethod.min_positive_value" title="min_positive_value">min_positive_value</a></li><li><a href="#tymethod.min_value" title="min_value">min_value</a></li><li><a href="#tymethod.mul_add" title="mul_add">mul_add</a></li><li><a href="#tymethod.powf" title="powf">powf</a></li><li><a href="#tymethod.powi" title="powi">powi</a></li><li><a href="#tymethod.recip" title="recip">recip</a></li><li><a href="#tymethod.round" title="round">round</a></li><li><a href="#tymethod.signum" title="signum">signum</a></li><li><a href="#tymethod.sin" title="sin">sin</a></li><li><a href="#tymethod.sin_cos" title="sin_cos">sin_cos</a></li><li><a href="#tymethod.sinh" title="sinh">sinh</a></li><li><a href="#tymethod.sqrt" title="sqrt">sqrt</a></li><li><a href="#tymethod.tan" title="tan">tan</a></li><li><a href="#tymethod.tanh" title="tanh">tanh</a></li><li><a href="#tymethod.to_degrees" title="to_degrees">to_degrees</a></li><li><a href="#tymethod.to_radians" title="to_radians">to_radians</a></li><li><a href="#tymethod.trunc" title="trunc">trunc</a></li></ul><h3><a href="#dyn-compatibility">Dyn Compatibility</a></h3><h3><a href="#implementors">Implementors</a></h3></section><div id="rustdoc-modnav"><h2><a href="index.html">In num_<wbr>traits::<wbr>real</a></h2></div></div></nav><div class="sidebar-resizer" title="Drag to resize sidebar"></div><main><div class="width-limiter"><section id="main-content" class="content"><div class="main-heading"><div class="rustdoc-breadcrumbs"><a href="../index.html">num_traits</a>::<wbr><a href="index.html">real</a></div><h1>Trait <span class="trait">Real</span> <button id="copy-path" title="Copy item path to clipboard">Copy item path</button></h1><rustdoc-toolbar></rustdoc-toolbar><span class="sub-heading"><a class="src" href="../../src/num_traits/real.rs.html#17-780">Source</a> </span></div><pre class="rust item-decl"><code>pub trait Real:
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<a class="trait" href="../trait.Num.html" title="trait num_traits::Num">Num</a>
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+ <a class="trait" href="https://doc.rust-lang.org/1.93.1/core/marker/trait.Copy.html" title="trait core::marker::Copy">Copy</a>
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+ <a class="trait" href="../cast/trait.NumCast.html" title="trait num_traits::cast::NumCast">NumCast</a>
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+ <a class="trait" href="https://doc.rust-lang.org/1.93.1/core/cmp/trait.PartialOrd.html" title="trait core::cmp::PartialOrd">PartialOrd</a>
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+ <a class="trait" href="https://doc.rust-lang.org/1.93.1/core/ops/arith/trait.Neg.html" title="trait core::ops::arith::Neg">Neg</a><Output = Self> {
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<details class="toggle type-contents-toggle"><summary class="hideme"><span>Show 47 methods</span></summary> // Required methods
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fn <a href="#tymethod.min_value" class="fn">min_value</a>() -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.min_positive_value" class="fn">min_positive_value</a>() -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.epsilon" class="fn">epsilon</a>() -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.max_value" class="fn">max_value</a>() -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.floor" class="fn">floor</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.ceil" class="fn">ceil</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.round" class="fn">round</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.trunc" class="fn">trunc</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.fract" class="fn">fract</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.abs" class="fn">abs</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.signum" class="fn">signum</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.is_sign_positive" class="fn">is_sign_positive</a>(self) -> <a class="primitive" href="https://doc.rust-lang.org/1.93.1/std/primitive.bool.html">bool</a>;
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<span class="item-spacer"></span> fn <a href="#tymethod.is_sign_negative" class="fn">is_sign_negative</a>(self) -> <a class="primitive" href="https://doc.rust-lang.org/1.93.1/std/primitive.bool.html">bool</a>;
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<span class="item-spacer"></span> fn <a href="#tymethod.mul_add" class="fn">mul_add</a>(self, a: Self, b: Self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.recip" class="fn">recip</a>(self) -> Self;
|
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<span class="item-spacer"></span> fn <a href="#tymethod.powi" class="fn">powi</a>(self, n: <a class="primitive" href="https://doc.rust-lang.org/1.93.1/std/primitive.i32.html">i32</a>) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.powf" class="fn">powf</a>(self, n: Self) -> Self;
|
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<span class="item-spacer"></span> fn <a href="#tymethod.sqrt" class="fn">sqrt</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.exp" class="fn">exp</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.exp2" class="fn">exp2</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.ln" class="fn">ln</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.log" class="fn">log</a>(self, base: Self) -> Self;
|
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<span class="item-spacer"></span> fn <a href="#tymethod.log2" class="fn">log2</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.log10" class="fn">log10</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.to_degrees" class="fn">to_degrees</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.to_radians" class="fn">to_radians</a>(self) -> Self;
|
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<span class="item-spacer"></span> fn <a href="#tymethod.max" class="fn">max</a>(self, other: Self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.min" class="fn">min</a>(self, other: Self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.abs_sub" class="fn">abs_sub</a>(self, other: Self) -> Self;
|
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<span class="item-spacer"></span> fn <a href="#tymethod.cbrt" class="fn">cbrt</a>(self) -> Self;
|
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<span class="item-spacer"></span> fn <a href="#tymethod.hypot" class="fn">hypot</a>(self, other: Self) -> Self;
|
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<span class="item-spacer"></span> fn <a href="#tymethod.sin" class="fn">sin</a>(self) -> Self;
|
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<span class="item-spacer"></span> fn <a href="#tymethod.cos" class="fn">cos</a>(self) -> Self;
|
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<span class="item-spacer"></span> fn <a href="#tymethod.tan" class="fn">tan</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.asin" class="fn">asin</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.acos" class="fn">acos</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.atan" class="fn">atan</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.atan2" class="fn">atan2</a>(self, other: Self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.sin_cos" class="fn">sin_cos</a>(self) -> (Self, Self);
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<span class="item-spacer"></span> fn <a href="#tymethod.exp_m1" class="fn">exp_m1</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.ln_1p" class="fn">ln_1p</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.sinh" class="fn">sinh</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.cosh" class="fn">cosh</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.tanh" class="fn">tanh</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.asinh" class="fn">asinh</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.acosh" class="fn">acosh</a>(self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.atanh" class="fn">atanh</a>(self) -> Self;
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</details>}</code></pre><details class="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
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floating-point-specific characteristics such as NaN and infinity.</p>
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<p>See <a href="https://en.wikipedia.org/wiki/Real_data_type">this Wikipedia article</a>
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for a list of data types that could meaningfully implement this trait.</p>
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<p>This trait is only available with the <code>std</code> feature, or with the <code>libm</code> feature otherwise.</p>
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</div></details><h2 id="required-methods" class="section-header">Required Methods<a href="#required-methods" class="anchor">§</a></h2><div class="methods"><details class="toggle method-toggle" open><summary><section id="tymethod.min_value" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#28">Source</a><h4 class="code-header">fn <a href="#tymethod.min_value" class="fn">min_value</a>() -> Self</h4></section></summary><div class="docblock"><p>Returns the smallest finite value that this type can represent.</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real;
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<span class="kw">use </span>std::f64;
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<span class="kw">let </span>x: f64 = Real::min_value();
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<span class="macro">assert_eq!</span>(x, f64::MIN);</code></pre></div></div></details><details class="toggle method-toggle" open><summary><section id="tymethod.min_positive_value" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#40">Source</a><h4 class="code-header">fn <a href="#tymethod.min_positive_value" class="fn">min_positive_value</a>() -> Self</h4></section></summary><div class="docblock"><p>Returns the smallest positive, normalized value that this type can represent.</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real;
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<span class="kw">use </span>std::f64;
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<span class="kw">let </span>x: f64 = Real::min_positive_value();
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<span class="macro">assert_eq!</span>(x, f64::MIN_POSITIVE);</code></pre></div></div></details><details class="toggle method-toggle" open><summary><section id="tymethod.epsilon" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#57">Source</a><h4 class="code-header">fn <a href="#tymethod.epsilon" class="fn">epsilon</a>() -> Self</h4></section></summary><div class="docblock"><p>Returns epsilon, a small positive value.</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real;
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<span class="kw">use </span>std::f64;
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<span class="kw">let </span>x: f64 = Real::epsilon();
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<span class="macro">assert_eq!</span>(x, f64::EPSILON);</code></pre></div><h5 id="panics"><a class="doc-anchor" href="#panics">§</a>Panics</h5>
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<p>The default implementation will panic if <code>f32::EPSILON</code> cannot
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be cast to <code>Self</code>.</p>
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</div></details><details class="toggle method-toggle" open><summary><section id="tymethod.max_value" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#68">Source</a><h4 class="code-header">fn <a href="#tymethod.max_value" class="fn">max_value</a>() -> Self</h4></section></summary><div class="docblock"><p>Returns the largest finite value that this type can represent.</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real;
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<span class="kw">use </span>std::f64;
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<span class="kw">let </span>x: f64 = Real::max_value();
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<span class="macro">assert_eq!</span>(x, f64::MAX);</code></pre></div></div></details><details class="toggle method-toggle" open><summary><section id="tymethod.floor" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#81">Source</a><h4 class="code-header">fn <a href="#tymethod.floor" class="fn">floor</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the largest integer less than or equal to a number.</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real;
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<span class="kw">let </span>f = <span class="number">3.99</span>;
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<span class="kw">let </span>g = <span class="number">3.0</span>;
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<span class="macro">assert_eq!</span>(f.floor(), <span class="number">3.0</span>);
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<span class="macro">assert_eq!</span>(g.floor(), <span class="number">3.0</span>);</code></pre></div></div></details><details class="toggle method-toggle" open><summary><section id="tymethod.ceil" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#94">Source</a><h4 class="code-header">fn <a href="#tymethod.ceil" class="fn">ceil</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the smallest integer greater than or equal to a number.</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real;
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<span class="kw">let </span>f = <span class="number">3.01</span>;
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<span class="kw">let </span>g = <span class="number">4.0</span>;
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<span class="macro">assert_eq!</span>(f.ceil(), <span class="number">4.0</span>);
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<span class="macro">assert_eq!</span>(g.ceil(), <span class="number">4.0</span>);</code></pre></div></div></details><details class="toggle method-toggle" open><summary><section id="tymethod.round" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#108">Source</a><h4 class="code-header">fn <a href="#tymethod.round" class="fn">round</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the nearest integer to a number. Round half-way cases away from
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<code>0.0</code>.</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real;
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<span class="kw">let </span>f = <span class="number">3.3</span>;
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<span class="kw">let </span>g = -<span class="number">3.3</span>;
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<span class="macro">assert_eq!</span>(f.round(), <span class="number">3.0</span>);
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<span class="macro">assert_eq!</span>(g.round(), -<span class="number">3.0</span>);</code></pre></div></div></details><details class="toggle method-toggle" open><summary><section id="tymethod.trunc" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#121">Source</a><h4 class="code-header">fn <a href="#tymethod.trunc" class="fn">trunc</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Return the integer part of a number.</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real;
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<span class="kw">let </span>f = <span class="number">3.3</span>;
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<span class="kw">let </span>g = -<span class="number">3.7</span>;
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<span class="macro">assert_eq!</span>(f.trunc(), <span class="number">3.0</span>);
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<span class="macro">assert_eq!</span>(g.trunc(), -<span class="number">3.0</span>);</code></pre></div></div></details><details class="toggle method-toggle" open><summary><section id="tymethod.fract" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#136">Source</a><h4 class="code-header">fn <a href="#tymethod.fract" class="fn">fract</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the fractional part of a number.</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real;
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<span class="kw">let </span>x = <span class="number">3.5</span>;
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<span class="kw">let </span>y = -<span class="number">3.5</span>;
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<span class="kw">let </span>abs_difference_x = (x.fract() - <span class="number">0.5</span>).abs();
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<span class="kw">let </span>abs_difference_y = (y.fract() - (-<span class="number">0.5</span>)).abs();
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<span class="macro">assert!</span>(abs_difference_x < <span class="number">1e-10</span>);
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<span class="macro">assert!</span>(abs_difference_y < <span class="number">1e-10</span>);</code></pre></div></div></details><details class="toggle method-toggle" open><summary><section id="tymethod.abs" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#156">Source</a><h4 class="code-header">fn <a href="#tymethod.abs" class="fn">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
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number is <code>Float::nan()</code>.</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>num_traits::real::Real;
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<span class="kw">use </span>std::f64;
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<span class="kw">let </span>x = <span class="number">3.5</span>;
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<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="toggle method-toggle" open><summary><section id="tymethod.signum" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#175">Source</a><h4 class="code-header">fn <a href="#tymethod.signum" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.is_sign_positive" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#193">Source</a><h4 class="code-header">fn <a href="#tymethod.is_sign_positive" class="fn">is_sign_positive</a>(self) -> <a class="primitive" href="https://doc.rust-lang.org/1.93.1/std/primitive.bool.html">bool</a></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="toggle method-toggle" open><summary><section id="tymethod.is_sign_negative" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#211">Source</a><h4 class="code-header">fn <a href="#tymethod.is_sign_negative" class="fn">is_sign_negative</a>(self) -> <a class="primitive" href="https://doc.rust-lang.org/1.93.1/std/primitive.bool.html">bool</a></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="toggle method-toggle" open><summary><section id="tymethod.mul_add" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#231">Source</a><h4 class="code-header">fn <a href="#tymethod.mul_add" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.recip" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#243">Source</a><h4 class="code-header">fn <a href="#tymethod.recip" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.powi" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#257">Source</a><h4 class="code-header">fn <a href="#tymethod.powi" class="fn">powi</a>(self, n: <a class="primitive" href="https://doc.rust-lang.org/1.93.1/std/primitive.i32.html">i32</a>) -> 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="toggle method-toggle" open><summary><section id="tymethod.powf" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#269">Source</a><h4 class="code-header">fn <a href="#tymethod.powf" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.sqrt" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#290">Source</a><h4 class="code-header">fn <a href="#tymethod.sqrt" class="fn">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 class="doc-anchor" href="#panics-1">§</a>Panics</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="toggle method-toggle" open><summary><section id="tymethod.exp" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#306">Source</a><h4 class="code-header">fn <a href="#tymethod.exp" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.exp2" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#320">Source</a><h4 class="code-header">fn <a href="#tymethod.exp2" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.ln" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#340">Source</a><h4 class="code-header">fn <a href="#tymethod.ln" class="fn">ln</a>(self) -> Self</h4></section></summary><div class="docblock"><p>Returns the natural logarithm of the number.</p>
|
||
<h5 id="panics-2"><a class="doc-anchor" href="#panics-2">§</a>Panics</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="toggle method-toggle" open><summary><section id="tymethod.log" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#363">Source</a><h4 class="code-header">fn <a href="#tymethod.log" class="fn">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 class="doc-anchor" href="#panics-3">§</a>Panics</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="toggle method-toggle" open><summary><section id="tymethod.log2" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#381">Source</a><h4 class="code-header">fn <a href="#tymethod.log2" class="fn">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 class="doc-anchor" href="#panics-4">§</a>Panics</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="toggle method-toggle" open><summary><section id="tymethod.log10" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#400">Source</a><h4 class="code-header">fn <a href="#tymethod.log10" class="fn">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 class="doc-anchor" href="#panics-5">§</a>Panics</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="toggle method-toggle" open><summary><section id="tymethod.to_degrees" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#413">Source</a><h4 class="code-header">fn <a href="#tymethod.to_degrees" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.to_radians" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#426">Source</a><h4 class="code-header">fn <a href="#tymethod.to_radians" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.max" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#438">Source</a><h4 class="code-header">fn <a href="#tymethod.max" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.min" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#450">Source</a><h4 class="code-header">fn <a href="#tymethod.min" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.abs_sub" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#469">Source</a><h4 class="code-header">fn <a href="#tymethod.abs_sub" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.cbrt" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#483">Source</a><h4 class="code-header">fn <a href="#tymethod.cbrt" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.hypot" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#499">Source</a><h4 class="code-header">fn <a href="#tymethod.hypot" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.sin" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#513">Source</a><h4 class="code-header">fn <a href="#tymethod.sin" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.cos" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#527">Source</a><h4 class="code-header">fn <a href="#tymethod.cos" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.tan" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#540">Source</a><h4 class="code-header">fn <a href="#tymethod.tan" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.asin" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#562">Source</a><h4 class="code-header">fn <a href="#tymethod.asin" class="fn">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 class="doc-anchor" href="#panics-6">§</a>Panics</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="toggle method-toggle" open><summary><section id="tymethod.acos" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#584">Source</a><h4 class="code-header">fn <a href="#tymethod.acos" class="fn">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 class="doc-anchor" href="#panics-7">§</a>Panics</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="toggle method-toggle" open><summary><section id="tymethod.atan" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#599">Source</a><h4 class="code-header">fn <a href="#tymethod.atan" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.atan2" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#628">Source</a><h4 class="code-header">fn <a href="#tymethod.atan2" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.sin_cos" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#646">Source</a><h4 class="code-header">fn <a href="#tymethod.sin_cos" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.exp_m1" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#661">Source</a><h4 class="code-header">fn <a href="#tymethod.exp_m1" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.ln_1p" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#682">Source</a><h4 class="code-header">fn <a href="#tymethod.ln_1p" class="fn">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 class="doc-anchor" href="#panics-8">§</a>Panics</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="toggle method-toggle" open><summary><section id="tymethod.sinh" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#700">Source</a><h4 class="code-header">fn <a href="#tymethod.sinh" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.cosh" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#718">Source</a><h4 class="code-header">fn <a href="#tymethod.cosh" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.tanh" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#736">Source</a><h4 class="code-header">fn <a href="#tymethod.tanh" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.asinh" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#750">Source</a><h4 class="code-header">fn <a href="#tymethod.asinh" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.acosh" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#764">Source</a><h4 class="code-header">fn <a href="#tymethod.acosh" class="fn">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="toggle method-toggle" open><summary><section id="tymethod.atanh" class="method"><a class="src rightside" href="../../src/num_traits/real.rs.html#779">Source</a><h4 class="code-header">fn <a href="#tymethod.atanh" class="fn">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="dyn-compatibility" class="section-header">Dyn Compatibility<a href="#dyn-compatibility" class="anchor">§</a></h2><div class="dyn-compatibility-info"><p>This trait is <b>not</b> <a href="https://doc.rust-lang.org/1.93.1/reference/items/traits.html#dyn-compatibility">dyn compatible</a>.</p><p><i>In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.</i></p></div><h2 id="implementors" class="section-header">Implementors<a href="#implementors" class="anchor">§</a></h2><div id="implementors-list"><section id="impl-Real-for-T" class="impl"><a class="src 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="../../trait.impl/num_traits/real/trait.Real.js" async></script></section></div></main></body></html> |