| <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/root/.cargo/registry/src/github.com-1ecc6299db9ec823/num-traits-0.2.15/src/real.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>real.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../normalize.css"><link rel="stylesheet" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../ayu.css" disabled><link rel="stylesheet" href="../../dark.css" disabled><link rel="stylesheet" href="../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../storage.js"></script><script defer src="../../source-script.js"></script><script defer src="../../source-files.js"></script><script defer src="../../main.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../favicon.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><a class="sidebar-logo" href="../../num_traits/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../num_traits/index.html"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span> |
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| </pre><pre class="rust"><code><span class="attribute">#![cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))] |
| |
| </span><span class="kw">use </span>core::ops::Neg; |
| |
| <span class="kw">use </span>{Float, Num, NumCast}; |
| |
| <span class="comment">// NOTE: These doctests have the same issue as those in src/float.rs. |
| // They're testing the inherent methods directly, and not those of `Real`. |
| |
| </span><span class="doccomment">/// A trait for real number types that do not necessarily have |
| /// floating-point-specific characteristics such as NaN and infinity. |
| /// |
| /// See [this Wikipedia article](https://en.wikipedia.org/wiki/Real_data_type) |
| /// for a list of data types that could meaningfully implement this trait. |
| /// |
| /// This trait is only available with the `std` feature, or with the `libm` feature otherwise. |
| </span><span class="kw">pub trait </span>Real: Num + Copy + NumCast + PartialOrd + Neg<Output = <span class="self">Self</span>> { |
| <span class="doccomment">/// Returns the smallest finite value that this type can represent. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// use std::f64; |
| /// |
| /// let x: f64 = Real::min_value(); |
| /// |
| /// assert_eq!(x, f64::MIN); |
| /// ``` |
| </span><span class="kw">fn </span>min_value() -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the smallest positive, normalized value that this type can represent. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// use std::f64; |
| /// |
| /// let x: f64 = Real::min_positive_value(); |
| /// |
| /// assert_eq!(x, f64::MIN_POSITIVE); |
| /// ``` |
| </span><span class="kw">fn </span>min_positive_value() -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns epsilon, a small positive value. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// use std::f64; |
| /// |
| /// let x: f64 = Real::epsilon(); |
| /// |
| /// assert_eq!(x, f64::EPSILON); |
| /// ``` |
| /// |
| /// # Panics |
| /// |
| /// The default implementation will panic if `f32::EPSILON` cannot |
| /// be cast to `Self`. |
| </span><span class="kw">fn </span>epsilon() -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the largest finite value that this type can represent. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// use std::f64; |
| /// |
| /// let x: f64 = Real::max_value(); |
| /// assert_eq!(x, f64::MAX); |
| /// ``` |
| </span><span class="kw">fn </span>max_value() -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the largest integer less than or equal to a number. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let f = 3.99; |
| /// let g = 3.0; |
| /// |
| /// assert_eq!(f.floor(), 3.0); |
| /// assert_eq!(g.floor(), 3.0); |
| /// ``` |
| </span><span class="kw">fn </span>floor(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the smallest integer greater than or equal to a number. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let f = 3.01; |
| /// let g = 4.0; |
| /// |
| /// assert_eq!(f.ceil(), 4.0); |
| /// assert_eq!(g.ceil(), 4.0); |
| /// ``` |
| </span><span class="kw">fn </span>ceil(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the nearest integer to a number. Round half-way cases away from |
| /// `0.0`. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let f = 3.3; |
| /// let g = -3.3; |
| /// |
| /// assert_eq!(f.round(), 3.0); |
| /// assert_eq!(g.round(), -3.0); |
| /// ``` |
| </span><span class="kw">fn </span>round(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Return the integer part of a number. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let f = 3.3; |
| /// let g = -3.7; |
| /// |
| /// assert_eq!(f.trunc(), 3.0); |
| /// assert_eq!(g.trunc(), -3.0); |
| /// ``` |
| </span><span class="kw">fn </span>trunc(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the fractional part of a number. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// 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><span class="kw">fn </span>fract(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Computes the absolute value of `self`. Returns `Float::nan()` if the |
| /// number is `Float::nan()`. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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!(::num_traits::Float::is_nan(f64::NAN.abs())); |
| /// ``` |
| </span><span class="kw">fn </span>abs(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns a number that represents the sign of `self`. |
| /// |
| /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()` |
| /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()` |
| /// - `Float::nan()` if the number is `Float::nan()` |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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><span class="kw">fn </span>signum(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns `true` if `self` is positive, including `+0.0`, |
| /// `Float::infinity()`, and with newer versions of Rust `f64::NAN`. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// use std::f64; |
| /// |
| /// let neg_nan: f64 = -f64::NAN; |
| /// |
| /// let f = 7.0; |
| /// let g = -7.0; |
| /// |
| /// assert!(f.is_sign_positive()); |
| /// assert!(!g.is_sign_positive()); |
| /// assert!(!neg_nan.is_sign_positive()); |
| /// ``` |
| </span><span class="kw">fn </span>is_sign_positive(<span class="self">self</span>) -> bool; |
| |
| <span class="doccomment">/// Returns `true` if `self` is negative, including `-0.0`, |
| /// `Float::neg_infinity()`, and with newer versions of Rust `-f64::NAN`. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// use std::f64; |
| /// |
| /// let nan: f64 = f64::NAN; |
| /// |
| /// let f = 7.0; |
| /// let g = -7.0; |
| /// |
| /// assert!(!f.is_sign_negative()); |
| /// assert!(g.is_sign_negative()); |
| /// assert!(!nan.is_sign_negative()); |
| /// ``` |
| </span><span class="kw">fn </span>is_sign_negative(<span class="self">self</span>) -> bool; |
| |
| <span class="doccomment">/// Fused multiply-add. Computes `(self * a) + b` with only one rounding |
| /// error, yielding a more accurate result than an unfused multiply-add. |
| /// |
| /// Using `mul_add` can be more performant than an unfused multiply-add if |
| /// the target architecture has a dedicated `fma` CPU instruction. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// 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><span class="kw">fn </span>mul_add(<span class="self">self</span>, a: <span class="self">Self</span>, b: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Take the reciprocal (inverse) of a number, `1/x`. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let x = 2.0; |
| /// let abs_difference = (x.recip() - (1.0/x)).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>recip(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Raise a number to an integer power. |
| /// |
| /// Using this function is generally faster than using `powf` |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let x = 2.0; |
| /// let abs_difference = (x.powi(2) - x*x).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>powi(<span class="self">self</span>, n: i32) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Raise a number to a real number power. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let x = 2.0; |
| /// let abs_difference = (x.powf(2.0) - x*x).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>powf(<span class="self">self</span>, n: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Take the square root of a number. |
| /// |
| /// Returns NaN if `self` is a negative floating-point number. |
| /// |
| /// # Panics |
| /// |
| /// If the implementing type doesn't support NaN, this method should panic if `self < 0`. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let positive = 4.0; |
| /// let negative = -4.0; |
| /// |
| /// let abs_difference = (positive.sqrt() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// assert!(::num_traits::Float::is_nan(negative.sqrt())); |
| /// ``` |
| </span><span class="kw">fn </span>sqrt(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns `e^(self)`, (the exponential function). |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// 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><span class="kw">fn </span>exp(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns `2^(self)`. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let f = 2.0; |
| /// |
| /// // 2^2 - 4 == 0 |
| /// let abs_difference = (f.exp2() - 4.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>exp2(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the natural logarithm of the number. |
| /// |
| /// # Panics |
| /// |
| /// If `self <= 0` and this type does not support a NaN representation, this function should panic. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// 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><span class="kw">fn </span>ln(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the logarithm of the number with respect to an arbitrary base. |
| /// |
| /// # Panics |
| /// |
| /// If `self <= 0` and this type does not support a NaN representation, this function should panic. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// 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><span class="kw">fn </span>log(<span class="self">self</span>, base: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the base 2 logarithm of the number. |
| /// |
| /// # Panics |
| /// |
| /// If `self <= 0` and this type does not support a NaN representation, this function should panic. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let two = 2.0; |
| /// |
| /// // log2(2) - 1 == 0 |
| /// let abs_difference = (two.log2() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>log2(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the base 10 logarithm of the number. |
| /// |
| /// # Panics |
| /// |
| /// If `self <= 0` and this type does not support a NaN representation, this function should panic. |
| /// |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let ten = 10.0; |
| /// |
| /// // log10(10) - 1 == 0 |
| /// let abs_difference = (ten.log10() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>log10(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Converts radians to degrees. |
| /// |
| /// ``` |
| /// use std::f64::consts; |
| /// |
| /// let angle = consts::PI; |
| /// |
| /// let abs_difference = (angle.to_degrees() - 180.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>to_degrees(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Converts degrees to radians. |
| /// |
| /// ``` |
| /// use std::f64::consts; |
| /// |
| /// let angle = 180.0_f64; |
| /// |
| /// let abs_difference = (angle.to_radians() - consts::PI).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>to_radians(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the maximum of the two numbers. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let x = 1.0; |
| /// let y = 2.0; |
| /// |
| /// assert_eq!(x.max(y), y); |
| /// ``` |
| </span><span class="kw">fn </span>max(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the minimum of the two numbers. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let x = 1.0; |
| /// let y = 2.0; |
| /// |
| /// assert_eq!(x.min(y), x); |
| /// ``` |
| </span><span class="kw">fn </span>min(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// The positive difference of two numbers. |
| /// |
| /// * If `self <= other`: `0:0` |
| /// * Else: `self - other` |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// 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><span class="kw">fn </span>abs_sub(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Take the cubic root of a number. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let x = 8.0; |
| /// |
| /// // x^(1/3) - 2 == 0 |
| /// let abs_difference = (x.cbrt() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>cbrt(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Calculate the length of the hypotenuse of a right-angle triangle given |
| /// legs of length `x` and `y`. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// 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><span class="kw">fn </span>hypot(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Computes the sine of a number (in radians). |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// use std::f64; |
| /// |
| /// let x = f64::consts::PI/2.0; |
| /// |
| /// let abs_difference = (x.sin() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>sin(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Computes the cosine of a number (in radians). |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// use std::f64; |
| /// |
| /// let x = 2.0*f64::consts::PI; |
| /// |
| /// let abs_difference = (x.cos() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>cos(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Computes the tangent of a number (in radians). |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// use std::f64; |
| /// |
| /// let x = f64::consts::PI/4.0; |
| /// let abs_difference = (x.tan() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-14); |
| /// ``` |
| </span><span class="kw">fn </span>tan(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// 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]. |
| /// |
| /// # Panics |
| /// |
| /// If this type does not support a NaN representation, this function should panic |
| /// if the number is outside the range [-1, 1]. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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><span class="kw">fn </span>asin(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// 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]. |
| /// |
| /// # Panics |
| /// |
| /// If this type does not support a NaN representation, this function should panic |
| /// if the number is outside the range [-1, 1]. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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><span class="kw">fn </span>acos(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Computes the arctangent of a number. Return value is in radians in the |
| /// range [-pi/2, pi/2]; |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let f = 1.0; |
| /// |
| /// // atan(tan(1)) |
| /// let abs_difference = (f.tan().atan() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>atan(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`). |
| /// |
| /// * `x = 0`, `y = 0`: `0` |
| /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]` |
| /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]` |
| /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)` |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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><span class="kw">fn </span>atan2(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Simultaneously computes the sine and cosine of the number, `x`. Returns |
| /// `(sin(x), cos(x))`. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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><span class="kw">fn </span>sin_cos(<span class="self">self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>); |
| |
| <span class="doccomment">/// Returns `e^(self) - 1` in a way that is accurate even if the |
| /// number is close to zero. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let x = 7.0; |
| /// |
| /// // e^(ln(7)) - 1 |
| /// let abs_difference = (x.ln().exp_m1() - 6.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| </span><span class="kw">fn </span>exp_m1(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns `ln(1+n)` (natural logarithm) more accurately than if |
| /// the operations were performed separately. |
| /// |
| /// # Panics |
| /// |
| /// If this type does not support a NaN representation, this function should panic |
| /// if `self-1 <= 0`. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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><span class="kw">fn </span>ln_1p(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Hyperbolic sine function. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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><span class="kw">fn </span>sinh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Hyperbolic cosine function. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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><span class="kw">fn </span>cosh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Hyperbolic tangent function. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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><span class="kw">fn </span>tanh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Inverse hyperbolic sine function. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let x = 1.0; |
| /// let f = x.sinh().asinh(); |
| /// |
| /// let abs_difference = (f - x).abs(); |
| /// |
| /// assert!(abs_difference < 1.0e-10); |
| /// ``` |
| </span><span class="kw">fn </span>asinh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Inverse hyperbolic cosine function. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// |
| /// let x = 1.0; |
| /// let f = x.cosh().acosh(); |
| /// |
| /// let abs_difference = (f - x).abs(); |
| /// |
| /// assert!(abs_difference < 1.0e-10); |
| /// ``` |
| </span><span class="kw">fn </span>acosh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Inverse hyperbolic tangent function. |
| /// |
| /// ``` |
| /// use num_traits::real::Real; |
| /// 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><span class="kw">fn </span>atanh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| } |
| |
| <span class="kw">impl</span><T: Float> Real <span class="kw">for </span>T { |
| <span class="macro">forward! </span>{ |
| Float::min_value() -> <span class="self">Self</span>; |
| Float::min_positive_value() -> <span class="self">Self</span>; |
| Float::epsilon() -> <span class="self">Self</span>; |
| Float::max_value() -> <span class="self">Self</span>; |
| } |
| <span class="macro">forward! </span>{ |
| Float::floor(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::ceil(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::round(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::trunc(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::fract(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::abs(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::signum(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::is_sign_positive(<span class="self">self</span>) -> bool; |
| Float::is_sign_negative(<span class="self">self</span>) -> bool; |
| Float::mul_add(<span class="self">self</span>, a: <span class="self">Self</span>, b: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| Float::recip(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::powi(<span class="self">self</span>, n: i32) -> <span class="self">Self</span>; |
| Float::powf(<span class="self">self</span>, n: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| Float::sqrt(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::exp(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::exp2(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::ln(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::log(<span class="self">self</span>, base: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| Float::log2(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::log10(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::to_degrees(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::to_radians(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::max(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| Float::min(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| Float::abs_sub(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| Float::cbrt(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::hypot(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| Float::sin(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::cos(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::tan(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::asin(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::acos(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::atan(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::atan2(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>; |
| Float::sin_cos(<span class="self">self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>); |
| Float::exp_m1(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::ln_1p(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::sinh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::cosh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::tanh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::asinh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::acosh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| Float::atanh(<span class="self">self</span>) -> <span class="self">Self</span>; |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="num_traits" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |