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<section id='main' class="content trait">
<h1 class='fqn'><span class='in-band'>Trait <a href='index.html'>num</a>::<wbr><a class='trait' href=''>Float</a></span><span class='out-of-band'><span id='render-detail'>
<a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">
[<span class='inner'>−</span>]
</a>
</span><a id='src-782' class='srclink' href='../num_traits/float/trait.Float.html?gotosrc=782' title='goto source code'>[src]</a></span></h1>
<pre class='rust trait'>pub trait Float: <a class='trait' href='https://doc.rust-lang.org/nightly/core/marker/trait.Copy.html' title='core::marker::Copy'>Copy</a> + <a class='trait' href='../num/traits/trait.NumCast.html' title='num::traits::NumCast'>NumCast</a> + <a class='trait' href='../num/traits/trait.Num.html' title='num::traits::Num'>Num</a> + <a class='trait' href='https://doc.rust-lang.org/nightly/core/ops/trait.Neg.html' title='core::ops::Neg'>Neg</a><Output=Self> + <a class='trait' href='https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html' title='core::cmp::PartialOrd'>PartialOrd</a><Self> {
fn <a href='#tymethod.nan' class='fnname'>nan</a>() -> Self;
fn <a href='#tymethod.infinity' class='fnname'>infinity</a>() -> Self;
fn <a href='#tymethod.neg_infinity' class='fnname'>neg_infinity</a>() -> Self;
fn <a href='#tymethod.neg_zero' class='fnname'>neg_zero</a>() -> Self;
fn <a href='#tymethod.min_value' class='fnname'>min_value</a>() -> Self;
fn <a href='#tymethod.min_positive_value' class='fnname'>min_positive_value</a>() -> Self;
fn <a href='#tymethod.max_value' class='fnname'>max_value</a>() -> Self;
fn <a href='#tymethod.is_nan' class='fnname'>is_nan</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a>;
fn <a href='#tymethod.is_infinite' class='fnname'>is_infinite</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a>;
fn <a href='#tymethod.is_finite' class='fnname'>is_finite</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a>;
fn <a href='#tymethod.is_normal' class='fnname'>is_normal</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a>;
fn <a href='#tymethod.classify' class='fnname'>classify</a>(self) -> <a class='enum' href='https://doc.rust-lang.org/nightly/core/num/enum.FpCategory.html' title='core::num::FpCategory'>FpCategory</a>;
fn <a href='#tymethod.floor' class='fnname'>floor</a>(self) -> Self;
fn <a href='#tymethod.ceil' class='fnname'>ceil</a>(self) -> Self;
fn <a href='#tymethod.round' class='fnname'>round</a>(self) -> Self;
fn <a href='#tymethod.trunc' class='fnname'>trunc</a>(self) -> Self;
fn <a href='#tymethod.fract' class='fnname'>fract</a>(self) -> Self;
fn <a href='#tymethod.abs' class='fnname'>abs</a>(self) -> Self;
fn <a href='#tymethod.signum' class='fnname'>signum</a>(self) -> Self;
fn <a href='#tymethod.is_sign_positive' class='fnname'>is_sign_positive</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a>;
fn <a href='#tymethod.is_sign_negative' class='fnname'>is_sign_negative</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a>;
fn <a href='#tymethod.mul_add' class='fnname'>mul_add</a>(self, a: Self, b: Self) -> Self;
fn <a href='#tymethod.recip' class='fnname'>recip</a>(self) -> Self;
fn <a href='#tymethod.powi' class='fnname'>powi</a>(self, n: <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.i32.html'>i32</a>) -> Self;
fn <a href='#tymethod.powf' class='fnname'>powf</a>(self, n: Self) -> Self;
fn <a href='#tymethod.sqrt' class='fnname'>sqrt</a>(self) -> Self;
fn <a href='#tymethod.exp' class='fnname'>exp</a>(self) -> Self;
fn <a href='#tymethod.exp2' class='fnname'>exp2</a>(self) -> Self;
fn <a href='#tymethod.ln' class='fnname'>ln</a>(self) -> Self;
fn <a href='#tymethod.log' class='fnname'>log</a>(self, base: Self) -> Self;
fn <a href='#tymethod.log2' class='fnname'>log2</a>(self) -> Self;
fn <a href='#tymethod.log10' class='fnname'>log10</a>(self) -> Self;
fn <a href='#tymethod.max' class='fnname'>max</a>(self, other: Self) -> Self;
fn <a href='#tymethod.min' class='fnname'>min</a>(self, other: Self) -> Self;
fn <a href='#tymethod.abs_sub' class='fnname'>abs_sub</a>(self, other: Self) -> Self;
fn <a href='#tymethod.cbrt' class='fnname'>cbrt</a>(self) -> Self;
fn <a href='#tymethod.hypot' class='fnname'>hypot</a>(self, other: Self) -> Self;
fn <a href='#tymethod.sin' class='fnname'>sin</a>(self) -> Self;
fn <a href='#tymethod.cos' class='fnname'>cos</a>(self) -> Self;
fn <a href='#tymethod.tan' class='fnname'>tan</a>(self) -> Self;
fn <a href='#tymethod.asin' class='fnname'>asin</a>(self) -> Self;
fn <a href='#tymethod.acos' class='fnname'>acos</a>(self) -> Self;
fn <a href='#tymethod.atan' class='fnname'>atan</a>(self) -> Self;
fn <a href='#tymethod.atan2' class='fnname'>atan2</a>(self, other: Self) -> Self;
fn <a href='#tymethod.sin_cos' class='fnname'>sin_cos</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.tuple.html'>(</a>Self, Self<a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.tuple.html'>)</a>;
fn <a href='#tymethod.exp_m1' class='fnname'>exp_m1</a>(self) -> Self;
fn <a href='#tymethod.ln_1p' class='fnname'>ln_1p</a>(self) -> Self;
fn <a href='#tymethod.sinh' class='fnname'>sinh</a>(self) -> Self;
fn <a href='#tymethod.cosh' class='fnname'>cosh</a>(self) -> Self;
fn <a href='#tymethod.tanh' class='fnname'>tanh</a>(self) -> Self;
fn <a href='#tymethod.asinh' class='fnname'>asinh</a>(self) -> Self;
fn <a href='#tymethod.acosh' class='fnname'>acosh</a>(self) -> Self;
fn <a href='#tymethod.atanh' class='fnname'>atanh</a>(self) -> Self;
fn <a href='#tymethod.integer_decode' class='fnname'>integer_decode</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.tuple.html'>(</a><a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.u64.html'>u64</a>, <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.i16.html'>i16</a>, <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.i8.html'>i8</a><a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.tuple.html'>)</a>;
}</pre>
<h2 id='required-methods'>Required Methods</h2>
<div class='methods'>
<h3 id='tymethod.nan' class='method stab '><span id='nan.v' class='invisible'><code>fn <a href='#tymethod.nan' class='fnname'>nan</a>() -> Self</code></span></h3><div class='docblock'><p>Returns the <code>NaN</code> value.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let nan: f32 = Float::nan();
assert!(nan.is_nan());
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>nan</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>nan</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>nan</span>.<span class='ident'>is_nan</span>());<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.infinity' class='method stab '><span id='infinity.v' class='invisible'><code>fn <a href='#tymethod.infinity' class='fnname'>infinity</a>() -> Self</code></span></h3><div class='docblock'><p>Returns the infinite value.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f32;
let infinity: f32 = Float::infinity();
assert!(infinity.is_infinite());
assert!(!infinity.is_finite());
assert!(infinity > f32::MAX);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f32</span>;
<span class='kw'>let</span> <span class='ident'>infinity</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>infinity</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>infinity</span>.<span class='ident'>is_infinite</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>infinity</span>.<span class='ident'>is_finite</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>infinity</span> <span class='op'>></span> <span class='ident'>f32</span>::<span class='ident'>MAX</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.neg_infinity' class='method stab '><span id='neg_infinity.v' class='invisible'><code>fn <a href='#tymethod.neg_infinity' class='fnname'>neg_infinity</a>() -> Self</code></span></h3><div class='docblock'><p>Returns the negative infinite value.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f32;
let neg_infinity: f32 = Float::neg_infinity();
assert!(neg_infinity.is_infinite());
assert!(!neg_infinity.is_finite());
assert!(neg_infinity < f32::MIN);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f32</span>;
<span class='kw'>let</span> <span class='ident'>neg_infinity</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>neg_infinity</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>neg_infinity</span>.<span class='ident'>is_infinite</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>neg_infinity</span>.<span class='ident'>is_finite</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>neg_infinity</span> <span class='op'><</span> <span class='ident'>f32</span>::<span class='ident'>MIN</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.neg_zero' class='method stab '><span id='neg_zero.v' class='invisible'><code>fn <a href='#tymethod.neg_zero' class='fnname'>neg_zero</a>() -> Self</code></span></h3><div class='docblock'><p>Returns <code>-0.0</code>.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::{Zero, Float};
let inf: f32 = Float::infinity();
let zero: f32 = Zero::zero();
let neg_zero: f32 = Float::neg_zero();
assert_eq!(zero, neg_zero);
assert_eq!(7.0f32/inf, zero);
assert_eq!(zero * 10.0, zero);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::{<span class='ident'>Zero</span>, <span class='ident'>Float</span>};
<span class='kw'>let</span> <span class='ident'>inf</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>infinity</span>();
<span class='kw'>let</span> <span class='ident'>zero</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>Zero</span>::<span class='ident'>zero</span>();
<span class='kw'>let</span> <span class='ident'>neg_zero</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>neg_zero</span>();
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>zero</span>, <span class='ident'>neg_zero</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='number'>7.0f32</span><span class='op'>/</span><span class='ident'>inf</span>, <span class='ident'>zero</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>zero</span> <span class='op'>*</span> <span class='number'>10.0</span>, <span class='ident'>zero</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.min_value' class='method stab '><span id='min_value.v' class='invisible'><code>fn <a href='#tymethod.min_value' class='fnname'>min_value</a>() -> Self</code></span></h3><div class='docblock'><p>Returns the smallest finite value that this type can represent.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let x: f64 = Float::min_value();
assert_eq!(x, f64::MIN);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>x</span>: <span class='ident'>f64</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>min_value</span>();
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>x</span>, <span class='ident'>f64</span>::<span class='ident'>MIN</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.min_positive_value' class='method stab '><span id='min_positive_value.v' class='invisible'><code>fn <a href='#tymethod.min_positive_value' class='fnname'>min_positive_value</a>() -> Self</code></span></h3><div class='docblock'><p>Returns the smallest positive, normalized value that this type can represent.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let x: f64 = Float::min_positive_value();
assert_eq!(x, f64::MIN_POSITIVE);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>x</span>: <span class='ident'>f64</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>min_positive_value</span>();
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>x</span>, <span class='ident'>f64</span>::<span class='ident'>MIN_POSITIVE</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.max_value' class='method stab '><span id='max_value.v' class='invisible'><code>fn <a href='#tymethod.max_value' class='fnname'>max_value</a>() -> Self</code></span></h3><div class='docblock'><p>Returns the largest finite value that this type can represent.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let x: f64 = Float::max_value();
assert_eq!(x, f64::MAX);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>x</span>: <span class='ident'>f64</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>max_value</span>();
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>x</span>, <span class='ident'>f64</span>::<span class='ident'>MAX</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.is_nan' class='method stab '><span id='is_nan.v' class='invisible'><code>fn <a href='#tymethod.is_nan' class='fnname'>is_nan</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a></code></span></h3><div class='docblock'><p>Returns <code>true</code> if this value is <code>NaN</code> and false otherwise.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let nan = f64::NAN;
let f = 7.0;
assert!(nan.is_nan());
assert!(!f.is_nan());
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>nan</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>NAN</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>7.0</span>;
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>nan</span>.<span class='ident'>is_nan</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>f</span>.<span class='ident'>is_nan</span>());<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.is_infinite' class='method stab '><span id='is_infinite.v' class='invisible'><code>fn <a href='#tymethod.is_infinite' class='fnname'>is_infinite</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a></code></span></h3><div class='docblock'><p>Returns <code>true</code> if this value is positive infinity or negative infinity and
false otherwise.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f32;
let f = 7.0f32;
let inf: f32 = Float::infinity();
let neg_inf: f32 = Float::neg_infinity();
let nan: f32 = f32::NAN;
assert!(!f.is_infinite());
assert!(!nan.is_infinite());
assert!(inf.is_infinite());
assert!(neg_inf.is_infinite());
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f32</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>7.0f32</span>;
<span class='kw'>let</span> <span class='ident'>inf</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>infinity</span>();
<span class='kw'>let</span> <span class='ident'>neg_inf</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>neg_infinity</span>();
<span class='kw'>let</span> <span class='ident'>nan</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>f32</span>::<span class='ident'>NAN</span>;
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>f</span>.<span class='ident'>is_infinite</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>nan</span>.<span class='ident'>is_infinite</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>inf</span>.<span class='ident'>is_infinite</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>neg_inf</span>.<span class='ident'>is_infinite</span>());<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.is_finite' class='method stab '><span id='is_finite.v' class='invisible'><code>fn <a href='#tymethod.is_finite' class='fnname'>is_finite</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a></code></span></h3><div class='docblock'><p>Returns <code>true</code> if this number is neither infinite nor <code>NaN</code>.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f32;
let f = 7.0f32;
let inf: f32 = Float::infinity();
let neg_inf: f32 = Float::neg_infinity();
let nan: f32 = f32::NAN;
assert!(f.is_finite());
assert!(!nan.is_finite());
assert!(!inf.is_finite());
assert!(!neg_inf.is_finite());
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f32</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>7.0f32</span>;
<span class='kw'>let</span> <span class='ident'>inf</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>infinity</span>();
<span class='kw'>let</span> <span class='ident'>neg_inf</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>neg_infinity</span>();
<span class='kw'>let</span> <span class='ident'>nan</span>: <span class='ident'>f32</span> <span class='op'>=</span> <span class='ident'>f32</span>::<span class='ident'>NAN</span>;
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>f</span>.<span class='ident'>is_finite</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>nan</span>.<span class='ident'>is_finite</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>inf</span>.<span class='ident'>is_finite</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>neg_inf</span>.<span class='ident'>is_finite</span>());<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.is_normal' class='method stab '><span id='is_normal.v' class='invisible'><code>fn <a href='#tymethod.is_normal' class='fnname'>is_normal</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a></code></span></h3><div class='docblock'><p>Returns <code>true</code> if the number is neither zero, infinite,
<a href="http://en.wikipedia.org/wiki/Denormal_number">subnormal</a>, or <code>NaN</code>.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f32;
let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
let max = f32::MAX;
let lower_than_min = 1.0e-40_f32;
let zero = 0.0f32;
assert!(min.is_normal());
assert!(max.is_normal());
assert!(!zero.is_normal());
assert!(!f32::NAN.is_normal());
assert!(!f32::INFINITY.is_normal());
// Values between `0` and `min` are Subnormal.
assert!(!lower_than_min.is_normal());
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f32</span>;
<span class='kw'>let</span> <span class='ident'>min</span> <span class='op'>=</span> <span class='ident'>f32</span>::<span class='ident'>MIN_POSITIVE</span>; <span class='comment'>// 1.17549435e-38f32</span>
<span class='kw'>let</span> <span class='ident'>max</span> <span class='op'>=</span> <span class='ident'>f32</span>::<span class='ident'>MAX</span>;
<span class='kw'>let</span> <span class='ident'>lower_than_min</span> <span class='op'>=</span> <span class='number'>1.0e-40_f32</span>;
<span class='kw'>let</span> <span class='ident'>zero</span> <span class='op'>=</span> <span class='number'>0.0f32</span>;
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>min</span>.<span class='ident'>is_normal</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>max</span>.<span class='ident'>is_normal</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>zero</span>.<span class='ident'>is_normal</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>f32</span>::<span class='ident'>NAN</span>.<span class='ident'>is_normal</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>f32</span>::<span class='ident'>INFINITY</span>.<span class='ident'>is_normal</span>());
<span class='comment'>// Values between `0` and `min` are Subnormal.</span>
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>lower_than_min</span>.<span class='ident'>is_normal</span>());<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.classify' class='method stab '><span id='classify.v' class='invisible'><code>fn <a href='#tymethod.classify' class='fnname'>classify</a>(self) -> <a class='enum' href='https://doc.rust-lang.org/nightly/core/num/enum.FpCategory.html' title='core::num::FpCategory'>FpCategory</a></code></span></h3><div class='docblock'><p>Returns the floating point category of the number. If only one property
is going to be tested, it is generally faster to use the specific
predicate instead.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::num::FpCategory;
use std::f32;
let num = 12.4f32;
let inf = f32::INFINITY;
assert_eq!(num.classify(), FpCategory::Normal);
assert_eq!(inf.classify(), FpCategory::Infinite);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>num</span>::<span class='ident'>FpCategory</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f32</span>;
<span class='kw'>let</span> <span class='ident'>num</span> <span class='op'>=</span> <span class='number'>12.4f32</span>;
<span class='kw'>let</span> <span class='ident'>inf</span> <span class='op'>=</span> <span class='ident'>f32</span>::<span class='ident'>INFINITY</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>num</span>.<span class='ident'>classify</span>(), <span class='ident'>FpCategory</span>::<span class='ident'>Normal</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>inf</span>.<span class='ident'>classify</span>(), <span class='ident'>FpCategory</span>::<span class='ident'>Infinite</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.floor' class='method stab '><span id='floor.v' class='invisible'><code>fn <a href='#tymethod.floor' class='fnname'>floor</a>(self) -> Self</code></span></h3><div class='docblock'><p>Returns the largest integer less than or equal to a number.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let f = 3.99;
let g = 3.0;
assert_eq!(f.floor(), 3.0);
assert_eq!(g.floor(), 3.0);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>3.99</span>;
<span class='kw'>let</span> <span class='ident'>g</span> <span class='op'>=</span> <span class='number'>3.0</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>f</span>.<span class='ident'>floor</span>(), <span class='number'>3.0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>g</span>.<span class='ident'>floor</span>(), <span class='number'>3.0</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.ceil' class='method stab '><span id='ceil.v' class='invisible'><code>fn <a href='#tymethod.ceil' class='fnname'>ceil</a>(self) -> Self</code></span></h3><div class='docblock'><p>Returns the smallest integer greater than or equal to a number.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let f = 3.01;
let g = 4.0;
assert_eq!(f.ceil(), 4.0);
assert_eq!(g.ceil(), 4.0);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>3.01</span>;
<span class='kw'>let</span> <span class='ident'>g</span> <span class='op'>=</span> <span class='number'>4.0</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>f</span>.<span class='ident'>ceil</span>(), <span class='number'>4.0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>g</span>.<span class='ident'>ceil</span>(), <span class='number'>4.0</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.round' class='method stab '><span id='round.v' class='invisible'><code>fn <a href='#tymethod.round' class='fnname'>round</a>(self) -> Self</code></span></h3><div class='docblock'><p>Returns the nearest integer to a number. Round half-way cases away from
<code>0.0</code>.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let f = 3.3;
let g = -3.3;
assert_eq!(f.round(), 3.0);
assert_eq!(g.round(), -3.0);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>3.3</span>;
<span class='kw'>let</span> <span class='ident'>g</span> <span class='op'>=</span> <span class='op'>-</span><span class='number'>3.3</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>f</span>.<span class='ident'>round</span>(), <span class='number'>3.0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>g</span>.<span class='ident'>round</span>(), <span class='op'>-</span><span class='number'>3.0</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.trunc' class='method stab '><span id='trunc.v' class='invisible'><code>fn <a href='#tymethod.trunc' class='fnname'>trunc</a>(self) -> Self</code></span></h3><div class='docblock'><p>Return the integer part of a number.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let f = 3.3;
let g = -3.7;
assert_eq!(f.trunc(), 3.0);
assert_eq!(g.trunc(), -3.0);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>3.3</span>;
<span class='kw'>let</span> <span class='ident'>g</span> <span class='op'>=</span> <span class='op'>-</span><span class='number'>3.7</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>f</span>.<span class='ident'>trunc</span>(), <span class='number'>3.0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>g</span>.<span class='ident'>trunc</span>(), <span class='op'>-</span><span class='number'>3.0</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.fract' class='method stab '><span id='fract.v' class='invisible'><code>fn <a href='#tymethod.fract' class='fnname'>fract</a>(self) -> Self</code></span></h3><div class='docblock'><p>Returns the fractional part of a number.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 3.5;
let y = -3.5;
let abs_difference_x = (x.fract() - 0.5).abs();
let abs_difference_y = (y.fract() - (-0.5)).abs();
assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>3.5</span>;
<span class='kw'>let</span> <span class='ident'>y</span> <span class='op'>=</span> <span class='op'>-</span><span class='number'>3.5</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference_x</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>fract</span>() <span class='op'>-</span> <span class='number'>0.5</span>).<span class='ident'>abs</span>();
<span class='kw'>let</span> <span class='ident'>abs_difference_y</span> <span class='op'>=</span> (<span class='ident'>y</span>.<span class='ident'>fract</span>() <span class='op'>-</span> (<span class='op'>-</span><span class='number'>0.5</span>)).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_x</span> <span class='op'><</span> <span class='number'>1e-10</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_y</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.abs' class='method stab '><span id='abs.v' class='invisible'><code>fn <a href='#tymethod.abs' class='fnname'>abs</a>(self) -> Self</code></span></h3><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>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let x = 3.5;
let y = -3.5;
let abs_difference_x = (x.abs() - x).abs();
let abs_difference_y = (y.abs() - (-y)).abs();
assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);
assert!(f64::NAN.abs().is_nan());
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>3.5</span>;
<span class='kw'>let</span> <span class='ident'>y</span> <span class='op'>=</span> <span class='op'>-</span><span class='number'>3.5</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference_x</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>abs</span>() <span class='op'>-</span> <span class='ident'>x</span>).<span class='ident'>abs</span>();
<span class='kw'>let</span> <span class='ident'>abs_difference_y</span> <span class='op'>=</span> (<span class='ident'>y</span>.<span class='ident'>abs</span>() <span class='op'>-</span> (<span class='op'>-</span><span class='ident'>y</span>)).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_x</span> <span class='op'><</span> <span class='number'>1e-10</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_y</span> <span class='op'><</span> <span class='number'>1e-10</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>f64</span>::<span class='ident'>NAN</span>.<span class='ident'>abs</span>().<span class='ident'>is_nan</span>());<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.signum' class='method stab '><span id='signum.v' class='invisible'><code>fn <a href='#tymethod.signum' class='fnname'>signum</a>(self) -> Self</code></span></h3><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>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let f = 3.5;
assert_eq!(f.signum(), 1.0);
assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
assert!(f64::NAN.signum().is_nan());
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>3.5</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>f</span>.<span class='ident'>signum</span>(), <span class='number'>1.0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>f64</span>::<span class='ident'>NEG_INFINITY</span>.<span class='ident'>signum</span>(), <span class='op'>-</span><span class='number'>1.0</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>f64</span>::<span class='ident'>NAN</span>.<span class='ident'>signum</span>().<span class='ident'>is_nan</span>());<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.is_sign_positive' class='method stab '><span id='is_sign_positive.v' class='invisible'><code>fn <a href='#tymethod.is_sign_positive' class='fnname'>is_sign_positive</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a></code></span></h3><div class='docblock'><p>Returns <code>true</code> if <code>self</code> is positive, including <code>+0.0</code> and
<code>Float::infinity()</code>.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let nan: f64 = f64::NAN;
let f = 7.0;
let g = -7.0;
assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());
// Requires both tests to determine if is `NaN`
assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>nan</span>: <span class='ident'>f64</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>NAN</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>7.0</span>;
<span class='kw'>let</span> <span class='ident'>g</span> <span class='op'>=</span> <span class='op'>-</span><span class='number'>7.0</span>;
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>f</span>.<span class='ident'>is_sign_positive</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>g</span>.<span class='ident'>is_sign_positive</span>());
<span class='comment'>// Requires both tests to determine if is `NaN`</span>
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>nan</span>.<span class='ident'>is_sign_positive</span>() <span class='op'>&&</span> <span class='op'>!</span><span class='ident'>nan</span>.<span class='ident'>is_sign_negative</span>());<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.is_sign_negative' class='method stab '><span id='is_sign_negative.v' class='invisible'><code>fn <a href='#tymethod.is_sign_negative' class='fnname'>is_sign_negative</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.bool.html'>bool</a></code></span></h3><div class='docblock'><p>Returns <code>true</code> if <code>self</code> is negative, including <code>-0.0</code> and
<code>Float::neg_infinity()</code>.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let nan = f64::NAN;
let f = 7.0;
let g = -7.0;
assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());
// Requires both tests to determine if is `NaN`.
assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>nan</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>NAN</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>7.0</span>;
<span class='kw'>let</span> <span class='ident'>g</span> <span class='op'>=</span> <span class='op'>-</span><span class='number'>7.0</span>;
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>f</span>.<span class='ident'>is_sign_negative</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>g</span>.<span class='ident'>is_sign_negative</span>());
<span class='comment'>// Requires both tests to determine if is `NaN`.</span>
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>nan</span>.<span class='ident'>is_sign_positive</span>() <span class='op'>&&</span> <span class='op'>!</span><span class='ident'>nan</span>.<span class='ident'>is_sign_negative</span>());<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.mul_add' class='method stab '><span id='mul_add.v' class='invisible'><code>fn <a href='#tymethod.mul_add' class='fnname'>mul_add</a>(self, a: Self, b: Self) -> Self</code></span></h3><div class='docblock'><p>Fused multiply-add. Computes <code>(self * a) + b</code> with only one rounding
error. This produces a more accurate result with better performance than
a separate multiplication operation followed by an add.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let m = 10.0;
let x = 4.0;
let b = 60.0;
// 100.0
let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>m</span> <span class='op'>=</span> <span class='number'>10.0</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>4.0</span>;
<span class='kw'>let</span> <span class='ident'>b</span> <span class='op'>=</span> <span class='number'>60.0</span>;
<span class='comment'>// 100.0</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>m</span>.<span class='ident'>mul_add</span>(<span class='ident'>x</span>, <span class='ident'>b</span>) <span class='op'>-</span> (<span class='ident'>m</span><span class='op'>*</span><span class='ident'>x</span> <span class='op'>+</span> <span class='ident'>b</span>)).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.recip' class='method stab '><span id='recip.v' class='invisible'><code>fn <a href='#tymethod.recip' class='fnname'>recip</a>(self) -> Self</code></span></h3><div class='docblock'><p>Take the reciprocal (inverse) of a number, <code>1/x</code>.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 2.0;
let abs_difference = (x.recip() - (1.0/x)).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>2.0</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>recip</span>() <span class='op'>-</span> (<span class='number'>1.0</span><span class='op'>/</span><span class='ident'>x</span>)).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.powi' class='method stab '><span id='powi.v' class='invisible'><code>fn <a href='#tymethod.powi' class='fnname'>powi</a>(self, n: <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.i32.html'>i32</a>) -> Self</code></span></h3><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>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 2.0;
let abs_difference = (x.powi(2) - x*x).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>2.0</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>powi</span>(<span class='number'>2</span>) <span class='op'>-</span> <span class='ident'>x</span><span class='op'>*</span><span class='ident'>x</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.powf' class='method stab '><span id='powf.v' class='invisible'><code>fn <a href='#tymethod.powf' class='fnname'>powf</a>(self, n: Self) -> Self</code></span></h3><div class='docblock'><p>Raise a number to a floating point power.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 2.0;
let abs_difference = (x.powf(2.0) - x*x).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>2.0</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>powf</span>(<span class='number'>2.0</span>) <span class='op'>-</span> <span class='ident'>x</span><span class='op'>*</span><span class='ident'>x</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.sqrt' class='method stab '><span id='sqrt.v' class='invisible'><code>fn <a href='#tymethod.sqrt' class='fnname'>sqrt</a>(self) -> Self</code></span></h3><div class='docblock'><p>Take the square root of a number.</p>
<p>Returns NaN if <code>self</code> is a negative number.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let positive = 4.0;
let negative = -4.0;
let abs_difference = (positive.sqrt() - 2.0).abs();
assert!(abs_difference < 1e-10);
assert!(negative.sqrt().is_nan());
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>positive</span> <span class='op'>=</span> <span class='number'>4.0</span>;
<span class='kw'>let</span> <span class='ident'>negative</span> <span class='op'>=</span> <span class='op'>-</span><span class='number'>4.0</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>positive</span>.<span class='ident'>sqrt</span>() <span class='op'>-</span> <span class='number'>2.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>negative</span>.<span class='ident'>sqrt</span>().<span class='ident'>is_nan</span>());<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.exp' class='method stab '><span id='exp.v' class='invisible'><code>fn <a href='#tymethod.exp' class='fnname'>exp</a>(self) -> Self</code></span></h3><div class='docblock'><p>Returns <code>e^(self)</code>, (the exponential function).</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let one = 1.0;
// e^1
let e = one.exp();
// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>one</span> <span class='op'>=</span> <span class='number'>1.0</span>;
<span class='comment'>// e^1</span>
<span class='kw'>let</span> <span class='ident'>e</span> <span class='op'>=</span> <span class='ident'>one</span>.<span class='ident'>exp</span>();
<span class='comment'>// ln(e) - 1 == 0</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>e</span>.<span class='ident'>ln</span>() <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.exp2' class='method stab '><span id='exp2.v' class='invisible'><code>fn <a href='#tymethod.exp2' class='fnname'>exp2</a>(self) -> Self</code></span></h3><div class='docblock'><p>Returns <code>2^(self)</code>.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let f = 2.0;
// 2^2 - 4 == 0
let abs_difference = (f.exp2() - 4.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>2.0</span>;
<span class='comment'>// 2^2 - 4 == 0</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>f</span>.<span class='ident'>exp2</span>() <span class='op'>-</span> <span class='number'>4.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.ln' class='method stab '><span id='ln.v' class='invisible'><code>fn <a href='#tymethod.ln' class='fnname'>ln</a>(self) -> Self</code></span></h3><div class='docblock'><p>Returns the natural logarithm of the number.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let one = 1.0;
// e^1
let e = one.exp();
// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>one</span> <span class='op'>=</span> <span class='number'>1.0</span>;
<span class='comment'>// e^1</span>
<span class='kw'>let</span> <span class='ident'>e</span> <span class='op'>=</span> <span class='ident'>one</span>.<span class='ident'>exp</span>();
<span class='comment'>// ln(e) - 1 == 0</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>e</span>.<span class='ident'>ln</span>() <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.log' class='method stab '><span id='log.v' class='invisible'><code>fn <a href='#tymethod.log' class='fnname'>log</a>(self, base: Self) -> Self</code></span></h3><div class='docblock'><p>Returns the logarithm of the number with respect to an arbitrary base.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let ten = 10.0;
let two = 2.0;
// log10(10) - 1 == 0
let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
// log2(2) - 1 == 0
let abs_difference_2 = (two.log(2.0) - 1.0).abs();
assert!(abs_difference_10 < 1e-10);
assert!(abs_difference_2 < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>ten</span> <span class='op'>=</span> <span class='number'>10.0</span>;
<span class='kw'>let</span> <span class='ident'>two</span> <span class='op'>=</span> <span class='number'>2.0</span>;
<span class='comment'>// log10(10) - 1 == 0</span>
<span class='kw'>let</span> <span class='ident'>abs_difference_10</span> <span class='op'>=</span> (<span class='ident'>ten</span>.<span class='ident'>log</span>(<span class='number'>10.0</span>) <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='comment'>// log2(2) - 1 == 0</span>
<span class='kw'>let</span> <span class='ident'>abs_difference_2</span> <span class='op'>=</span> (<span class='ident'>two</span>.<span class='ident'>log</span>(<span class='number'>2.0</span>) <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_10</span> <span class='op'><</span> <span class='number'>1e-10</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_2</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.log2' class='method stab '><span id='log2.v' class='invisible'><code>fn <a href='#tymethod.log2' class='fnname'>log2</a>(self) -> Self</code></span></h3><div class='docblock'><p>Returns the base 2 logarithm of the number.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let two = 2.0;
// log2(2) - 1 == 0
let abs_difference = (two.log2() - 1.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>two</span> <span class='op'>=</span> <span class='number'>2.0</span>;
<span class='comment'>// log2(2) - 1 == 0</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>two</span>.<span class='ident'>log2</span>() <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.log10' class='method stab '><span id='log10.v' class='invisible'><code>fn <a href='#tymethod.log10' class='fnname'>log10</a>(self) -> Self</code></span></h3><div class='docblock'><p>Returns the base 10 logarithm of the number.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let ten = 10.0;
// log10(10) - 1 == 0
let abs_difference = (ten.log10() - 1.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>ten</span> <span class='op'>=</span> <span class='number'>10.0</span>;
<span class='comment'>// log10(10) - 1 == 0</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>ten</span>.<span class='ident'>log10</span>() <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.max' class='method stab '><span id='max.v' class='invisible'><code>fn <a href='#tymethod.max' class='fnname'>max</a>(self, other: Self) -> Self</code></span></h3><div class='docblock'><p>Returns the maximum of the two numbers.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 1.0;
let y = 2.0;
assert_eq!(x.max(y), y);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>1.0</span>;
<span class='kw'>let</span> <span class='ident'>y</span> <span class='op'>=</span> <span class='number'>2.0</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>x</span>.<span class='ident'>max</span>(<span class='ident'>y</span>), <span class='ident'>y</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.min' class='method stab '><span id='min.v' class='invisible'><code>fn <a href='#tymethod.min' class='fnname'>min</a>(self, other: Self) -> Self</code></span></h3><div class='docblock'><p>Returns the minimum of the two numbers.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 1.0;
let y = 2.0;
assert_eq!(x.min(y), x);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>1.0</span>;
<span class='kw'>let</span> <span class='ident'>y</span> <span class='op'>=</span> <span class='number'>2.0</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>x</span>.<span class='ident'>min</span>(<span class='ident'>y</span>), <span class='ident'>x</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.abs_sub' class='method stab '><span id='abs_sub.v' class='invisible'><code>fn <a href='#tymethod.abs_sub' class='fnname'>abs_sub</a>(self, other: Self) -> Self</code></span></h3><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>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 3.0;
let y = -3.0;
let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>3.0</span>;
<span class='kw'>let</span> <span class='ident'>y</span> <span class='op'>=</span> <span class='op'>-</span><span class='number'>3.0</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference_x</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>abs_sub</span>(<span class='number'>1.0</span>) <span class='op'>-</span> <span class='number'>2.0</span>).<span class='ident'>abs</span>();
<span class='kw'>let</span> <span class='ident'>abs_difference_y</span> <span class='op'>=</span> (<span class='ident'>y</span>.<span class='ident'>abs_sub</span>(<span class='number'>1.0</span>) <span class='op'>-</span> <span class='number'>0.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_x</span> <span class='op'><</span> <span class='number'>1e-10</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_y</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.cbrt' class='method stab '><span id='cbrt.v' class='invisible'><code>fn <a href='#tymethod.cbrt' class='fnname'>cbrt</a>(self) -> Self</code></span></h3><div class='docblock'><p>Take the cubic root of a number.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 8.0;
// x^(1/3) - 2 == 0
let abs_difference = (x.cbrt() - 2.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>8.0</span>;
<span class='comment'>// x^(1/3) - 2 == 0</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>cbrt</span>() <span class='op'>-</span> <span class='number'>2.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.hypot' class='method stab '><span id='hypot.v' class='invisible'><code>fn <a href='#tymethod.hypot' class='fnname'>hypot</a>(self, other: Self) -> Self</code></span></h3><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>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 2.0;
let y = 3.0;
// sqrt(x^2 + y^2)
let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>2.0</span>;
<span class='kw'>let</span> <span class='ident'>y</span> <span class='op'>=</span> <span class='number'>3.0</span>;
<span class='comment'>// sqrt(x^2 + y^2)</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>hypot</span>(<span class='ident'>y</span>) <span class='op'>-</span> (<span class='ident'>x</span>.<span class='ident'>powi</span>(<span class='number'>2</span>) <span class='op'>+</span> <span class='ident'>y</span>.<span class='ident'>powi</span>(<span class='number'>2</span>)).<span class='ident'>sqrt</span>()).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.sin' class='method stab '><span id='sin.v' class='invisible'><code>fn <a href='#tymethod.sin' class='fnname'>sin</a>(self) -> Self</code></span></h3><div class='docblock'><p>Computes the sine of a number (in radians).</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let x = f64::consts::PI/2.0;
let abs_difference = (x.sin() - 1.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span><span class='op'>/</span><span class='number'>2.0</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>sin</span>() <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.cos' class='method stab '><span id='cos.v' class='invisible'><code>fn <a href='#tymethod.cos' class='fnname'>cos</a>(self) -> Self</code></span></h3><div class='docblock'><p>Computes the cosine of a number (in radians).</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let x = 2.0*f64::consts::PI;
let abs_difference = (x.cos() - 1.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>2.0</span><span class='op'>*</span><span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>cos</span>() <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.tan' class='method stab '><span id='tan.v' class='invisible'><code>fn <a href='#tymethod.tan' class='fnname'>tan</a>(self) -> Self</code></span></h3><div class='docblock'><p>Computes the tangent of a number (in radians).</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let x = f64::consts::PI/4.0;
let abs_difference = (x.tan() - 1.0).abs();
assert!(abs_difference < 1e-14);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span><span class='op'>/</span><span class='number'>4.0</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>tan</span>() <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-14</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.asin' class='method stab '><span id='asin.v' class='invisible'><code>fn <a href='#tymethod.asin' class='fnname'>asin</a>(self) -> Self</code></span></h3><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>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let f = f64::consts::PI / 2.0;
// asin(sin(pi/2))
let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span> <span class='op'>/</span> <span class='number'>2.0</span>;
<span class='comment'>// asin(sin(pi/2))</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>f</span>.<span class='ident'>sin</span>().<span class='ident'>asin</span>() <span class='op'>-</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span> <span class='op'>/</span> <span class='number'>2.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.acos' class='method stab '><span id='acos.v' class='invisible'><code>fn <a href='#tymethod.acos' class='fnname'>acos</a>(self) -> Self</code></span></h3><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>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let f = f64::consts::PI / 4.0;
// acos(cos(pi/4))
let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span> <span class='op'>/</span> <span class='number'>4.0</span>;
<span class='comment'>// acos(cos(pi/4))</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>f</span>.<span class='ident'>cos</span>().<span class='ident'>acos</span>() <span class='op'>-</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span> <span class='op'>/</span> <span class='number'>4.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.atan' class='method stab '><span id='atan.v' class='invisible'><code>fn <a href='#tymethod.atan' class='fnname'>atan</a>(self) -> Self</code></span></h3><div class='docblock'><p>Computes the arctangent of a number. Return value is in radians in the
range [-pi/2, pi/2];</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let f = 1.0;
// atan(tan(1))
let abs_difference = (f.tan().atan() - 1.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='number'>1.0</span>;
<span class='comment'>// atan(tan(1))</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>f</span>.<span class='ident'>tan</span>().<span class='ident'>atan</span>() <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.atan2' class='method stab '><span id='atan2.v' class='invisible'><code>fn <a href='#tymethod.atan2' class='fnname'>atan2</a>(self, other: Self) -> Self</code></span></h3><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>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let pi = f64::consts::PI;
// All angles from horizontal right (+x)
// 45 deg counter-clockwise
let x1 = 3.0;
let y1 = -3.0;
// 135 deg clockwise
let x2 = -3.0;
let y2 = 3.0;
let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
assert!(abs_difference_1 < 1e-10);
assert!(abs_difference_2 < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>pi</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span>;
<span class='comment'>// All angles from horizontal right (+x)</span>
<span class='comment'>// 45 deg counter-clockwise</span>
<span class='kw'>let</span> <span class='ident'>x1</span> <span class='op'>=</span> <span class='number'>3.0</span>;
<span class='kw'>let</span> <span class='ident'>y1</span> <span class='op'>=</span> <span class='op'>-</span><span class='number'>3.0</span>;
<span class='comment'>// 135 deg clockwise</span>
<span class='kw'>let</span> <span class='ident'>x2</span> <span class='op'>=</span> <span class='op'>-</span><span class='number'>3.0</span>;
<span class='kw'>let</span> <span class='ident'>y2</span> <span class='op'>=</span> <span class='number'>3.0</span>;
<span class='kw'>let</span> <span class='ident'>abs_difference_1</span> <span class='op'>=</span> (<span class='ident'>y1</span>.<span class='ident'>atan2</span>(<span class='ident'>x1</span>) <span class='op'>-</span> (<span class='op'>-</span><span class='ident'>pi</span><span class='op'>/</span><span class='number'>4.0</span>)).<span class='ident'>abs</span>();
<span class='kw'>let</span> <span class='ident'>abs_difference_2</span> <span class='op'>=</span> (<span class='ident'>y2</span>.<span class='ident'>atan2</span>(<span class='ident'>x2</span>) <span class='op'>-</span> <span class='number'>3.0</span><span class='op'>*</span><span class='ident'>pi</span><span class='op'>/</span><span class='number'>4.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_1</span> <span class='op'><</span> <span class='number'>1e-10</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_2</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.sin_cos' class='method stab '><span id='sin_cos.v' class='invisible'><code>fn <a href='#tymethod.sin_cos' class='fnname'>sin_cos</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.tuple.html'>(</a>Self, Self<a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.tuple.html'>)</a></code></span></h3><div class='docblock'><p>Simultaneously computes the sine and cosine of the number, <code>x</code>. Returns
<code>(sin(x), cos(x))</code>.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let x = f64::consts::PI/4.0;
let f = x.sin_cos();
let abs_difference_0 = (f.0 - x.sin()).abs();
let abs_difference_1 = (f.1 - x.cos()).abs();
assert!(abs_difference_0 < 1e-10);
assert!(abs_difference_0 < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span><span class='op'>/</span><span class='number'>4.0</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='ident'>x</span>.<span class='ident'>sin_cos</span>();
<span class='kw'>let</span> <span class='ident'>abs_difference_0</span> <span class='op'>=</span> (<span class='ident'>f</span>.<span class='number'>0</span> <span class='op'>-</span> <span class='ident'>x</span>.<span class='ident'>sin</span>()).<span class='ident'>abs</span>();
<span class='kw'>let</span> <span class='ident'>abs_difference_1</span> <span class='op'>=</span> (<span class='ident'>f</span>.<span class='number'>1</span> <span class='op'>-</span> <span class='ident'>x</span>.<span class='ident'>cos</span>()).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_0</span> <span class='op'><</span> <span class='number'>1e-10</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference_0</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.exp_m1' class='method stab '><span id='exp_m1.v' class='invisible'><code>fn <a href='#tymethod.exp_m1' class='fnname'>exp_m1</a>(self) -> Self</code></span></h3><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>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 7.0;
// e^(ln(7)) - 1
let abs_difference = (x.ln().exp_m1() - 6.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>7.0</span>;
<span class='comment'>// e^(ln(7)) - 1</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>ln</span>().<span class='ident'>exp_m1</span>() <span class='op'>-</span> <span class='number'>6.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.ln_1p' class='method stab '><span id='ln_1p.v' class='invisible'><code>fn <a href='#tymethod.ln_1p' class='fnname'>ln_1p</a>(self) -> Self</code></span></h3><div class='docblock'><p>Returns <code>ln(1+n)</code> (natural logarithm) more accurately than if
the operations were performed separately.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let x = f64::consts::E - 1.0;
// ln(1 + (e - 1)) == ln(e) == 1
let abs_difference = (x.ln_1p() - 1.0).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>E</span> <span class='op'>-</span> <span class='number'>1.0</span>;
<span class='comment'>// ln(1 + (e - 1)) == ln(e) == 1</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>x</span>.<span class='ident'>ln_1p</span>() <span class='op'>-</span> <span class='number'>1.0</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.sinh' class='method stab '><span id='sinh.v' class='invisible'><code>fn <a href='#tymethod.sinh' class='fnname'>sinh</a>(self) -> Self</code></span></h3><div class='docblock'><p>Hyperbolic sine function.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let e = f64::consts::E;
let x = 1.0;
let f = x.sinh();
// Solving sinh() at 1 gives `(e^2-1)/(2e)`
let g = (e*e - 1.0)/(2.0*e);
let abs_difference = (f - g).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>e</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>E</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>1.0</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='ident'>x</span>.<span class='ident'>sinh</span>();
<span class='comment'>// Solving sinh() at 1 gives `(e^2-1)/(2e)`</span>
<span class='kw'>let</span> <span class='ident'>g</span> <span class='op'>=</span> (<span class='ident'>e</span><span class='op'>*</span><span class='ident'>e</span> <span class='op'>-</span> <span class='number'>1.0</span>)<span class='op'>/</span>(<span class='number'>2.0</span><span class='op'>*</span><span class='ident'>e</span>);
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>f</span> <span class='op'>-</span> <span class='ident'>g</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.cosh' class='method stab '><span id='cosh.v' class='invisible'><code>fn <a href='#tymethod.cosh' class='fnname'>cosh</a>(self) -> Self</code></span></h3><div class='docblock'><p>Hyperbolic cosine function.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let e = f64::consts::E;
let x = 1.0;
let f = x.cosh();
// Solving cosh() at 1 gives this result
let g = (e*e + 1.0)/(2.0*e);
let abs_difference = (f - g).abs();
// Same result
assert!(abs_difference < 1.0e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>e</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>E</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>1.0</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='ident'>x</span>.<span class='ident'>cosh</span>();
<span class='comment'>// Solving cosh() at 1 gives this result</span>
<span class='kw'>let</span> <span class='ident'>g</span> <span class='op'>=</span> (<span class='ident'>e</span><span class='op'>*</span><span class='ident'>e</span> <span class='op'>+</span> <span class='number'>1.0</span>)<span class='op'>/</span>(<span class='number'>2.0</span><span class='op'>*</span><span class='ident'>e</span>);
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>f</span> <span class='op'>-</span> <span class='ident'>g</span>).<span class='ident'>abs</span>();
<span class='comment'>// Same result</span>
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1.0e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.tanh' class='method stab '><span id='tanh.v' class='invisible'><code>fn <a href='#tymethod.tanh' class='fnname'>tanh</a>(self) -> Self</code></span></h3><div class='docblock'><p>Hyperbolic tangent function.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let e = f64::consts::E;
let x = 1.0;
let f = x.tanh();
// Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
let abs_difference = (f - g).abs();
assert!(abs_difference < 1.0e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>e</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>E</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>1.0</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='ident'>x</span>.<span class='ident'>tanh</span>();
<span class='comment'>// Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`</span>
<span class='kw'>let</span> <span class='ident'>g</span> <span class='op'>=</span> (<span class='number'>1.0</span> <span class='op'>-</span> <span class='ident'>e</span>.<span class='ident'>powi</span>(<span class='op'>-</span><span class='number'>2</span>))<span class='op'>/</span>(<span class='number'>1.0</span> <span class='op'>+</span> <span class='ident'>e</span>.<span class='ident'>powi</span>(<span class='op'>-</span><span class='number'>2</span>));
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>f</span> <span class='op'>-</span> <span class='ident'>g</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1.0e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.asinh' class='method stab '><span id='asinh.v' class='invisible'><code>fn <a href='#tymethod.asinh' class='fnname'>asinh</a>(self) -> Self</code></span></h3><div class='docblock'><p>Inverse hyperbolic sine function.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 1.0;
let f = x.sinh().asinh();
let abs_difference = (f - x).abs();
assert!(abs_difference < 1.0e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>1.0</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='ident'>x</span>.<span class='ident'>sinh</span>().<span class='ident'>asinh</span>();
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>f</span> <span class='op'>-</span> <span class='ident'>x</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1.0e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.acosh' class='method stab '><span id='acosh.v' class='invisible'><code>fn <a href='#tymethod.acosh' class='fnname'>acosh</a>(self) -> Self</code></span></h3><div class='docblock'><p>Inverse hyperbolic cosine function.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let x = 1.0;
let f = x.cosh().acosh();
let abs_difference = (f - x).abs();
assert!(abs_difference < 1.0e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='number'>1.0</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='ident'>x</span>.<span class='ident'>cosh</span>().<span class='ident'>acosh</span>();
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>f</span> <span class='op'>-</span> <span class='ident'>x</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1.0e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.atanh' class='method stab '><span id='atanh.v' class='invisible'><code>fn <a href='#tymethod.atanh' class='fnname'>atanh</a>(self) -> Self</code></span></h3><div class='docblock'><p>Inverse hyperbolic tangent function.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
use std::f64;
let e = f64::consts::E;
let f = e.tanh().atanh();
let abs_difference = (f - e).abs();
assert!(abs_difference < 1.0e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>f64</span>;
<span class='kw'>let</span> <span class='ident'>e</span> <span class='op'>=</span> <span class='ident'>f64</span>::<span class='ident'>consts</span>::<span class='ident'>E</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> <span class='ident'>e</span>.<span class='ident'>tanh</span>().<span class='ident'>atanh</span>();
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>f</span> <span class='op'>-</span> <span class='ident'>e</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1.0e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div><h3 id='tymethod.integer_decode' class='method stab '><span id='integer_decode.v' class='invisible'><code>fn <a href='#tymethod.integer_decode' class='fnname'>integer_decode</a>(self) -> <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.tuple.html'>(</a><a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.u64.html'>u64</a>, <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.i16.html'>i16</a>, <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.i8.html'>i8</a><a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.tuple.html'>)</a></code></span></h3><div class='docblock'><p>Returns the mantissa, base 2 exponent, and sign as integers, respectively.
The original number can be recovered by <code>sign * mantissa * 2 ^ exponent</code>.
The floating point encoding is documented in the <a href="../../../../../reference.html#machine-types">Reference</a>.</p>
<span class='rusttest'>extern crate num;
fn main() {
use num_traits::Float;
let num = 2.0f32;
// (8388608, -22, 1)
let (mantissa, exponent, sign) = Float::integer_decode(num);
let sign_f = sign as f32;
let mantissa_f = mantissa as f32;
let exponent_f = num.powf(exponent as f32);
// 1 * 8388608 * 2^(-22) == 2
let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
assert!(abs_difference < 1e-10);
}</span><pre class='rust rust-example-rendered'>
<span class='kw'>use</span> <span class='ident'>num_traits</span>::<span class='ident'>Float</span>;
<span class='kw'>let</span> <span class='ident'>num</span> <span class='op'>=</span> <span class='number'>2.0f32</span>;
<span class='comment'>// (8388608, -22, 1)</span>
<span class='kw'>let</span> (<span class='ident'>mantissa</span>, <span class='ident'>exponent</span>, <span class='ident'>sign</span>) <span class='op'>=</span> <span class='ident'>Float</span>::<span class='ident'>integer_decode</span>(<span class='ident'>num</span>);
<span class='kw'>let</span> <span class='ident'>sign_f</span> <span class='op'>=</span> <span class='ident'>sign</span> <span class='kw'>as</span> <span class='ident'>f32</span>;
<span class='kw'>let</span> <span class='ident'>mantissa_f</span> <span class='op'>=</span> <span class='ident'>mantissa</span> <span class='kw'>as</span> <span class='ident'>f32</span>;
<span class='kw'>let</span> <span class='ident'>exponent_f</span> <span class='op'>=</span> <span class='ident'>num</span>.<span class='ident'>powf</span>(<span class='ident'>exponent</span> <span class='kw'>as</span> <span class='ident'>f32</span>);
<span class='comment'>// 1 * 8388608 * 2^(-22) == 2</span>
<span class='kw'>let</span> <span class='ident'>abs_difference</span> <span class='op'>=</span> (<span class='ident'>sign_f</span> <span class='op'>*</span> <span class='ident'>mantissa_f</span> <span class='op'>*</span> <span class='ident'>exponent_f</span> <span class='op'>-</span> <span class='ident'>num</span>).<span class='ident'>abs</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>abs_difference</span> <span class='op'><</span> <span class='number'>1e-10</span>);<a class='test-arrow' target='_blank' href=''>Run</a></pre>
</div></div>
<h2 id='implementors'>Implementors</h2>
<ul class='item-list' id='implementors-list'>
<li><code>impl Float for <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.f32.html'>f32</a></code></li>
<li><code>impl Float for <a class='primitive' href='https://doc.rust-lang.org/nightly/std/primitive.f64.html'>f64</a></code></li>
</ul><script type="text/javascript" async
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