| <!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-complex-0.3.1/src/lib.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>lib.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_complex/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_complex/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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| <span id="2621">2621</span> |
| <span id="2622">2622</span> |
| <span id="2623">2623</span> |
| <span id="2624">2624</span> |
| <span id="2625">2625</span> |
| <span id="2626">2626</span> |
| <span id="2627">2627</span> |
| <span id="2628">2628</span> |
| <span id="2629">2629</span> |
| <span id="2630">2630</span> |
| <span id="2631">2631</span> |
| <span id="2632">2632</span> |
| <span id="2633">2633</span> |
| <span id="2634">2634</span> |
| <span id="2635">2635</span> |
| <span id="2636">2636</span> |
| </pre><pre class="rust"><code><span class="comment">// Copyright 2013 The Rust Project Developers. See the COPYRIGHT |
| // file at the top-level directory of this distribution and at |
| // http://rust-lang.org/COPYRIGHT. |
| // |
| // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or |
| // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license |
| // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your |
| // option. This file may not be copied, modified, or distributed |
| // except according to those terms. |
| |
| </span><span class="doccomment">//! Complex numbers. |
| //! |
| //! ## Compatibility |
| //! |
| //! The `num-complex` crate is tested for rustc 1.31 and greater. |
| |
| </span><span class="attribute">#![doc(html_root_url = <span class="string">"https://docs.rs/num-complex/0.3"</span>)] |
| #![no_std] |
| |
| #[cfg(any(test, feature = <span class="string">"std"</span>))] |
| #[cfg_attr(test, macro_use)] |
| </span><span class="kw">extern crate </span>std; |
| |
| <span class="kw">use </span>core::fmt; |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">use </span>core::hash; |
| <span class="kw">use </span>core::iter::{Product, Sum}; |
| <span class="kw">use </span>core::ops::{Add, Div, Mul, Neg, Rem, Sub}; |
| <span class="kw">use </span>core::str::FromStr; |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| </span><span class="kw">use </span>std::error::Error; |
| |
| <span class="kw">use </span>num_traits::{Inv, MulAdd, Num, One, Pow, Signed, Zero}; |
| |
| <span class="attribute">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))] |
| </span><span class="kw">use </span>num_traits::float::Float; |
| <span class="kw">use </span>num_traits::float::FloatCore; |
| |
| <span class="kw">mod </span>cast; |
| <span class="kw">mod </span>pow; |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"rand"</span>)] |
| </span><span class="kw">mod </span>crand; |
| <span class="attribute">#[cfg(feature = <span class="string">"rand"</span>)] |
| </span><span class="kw">pub use </span><span class="kw">crate</span>::crand::ComplexDistribution; |
| |
| <span class="comment">// FIXME #1284: handle complex NaN & infinity etc. This |
| // probably doesn't map to C's _Complex correctly. |
| |
| </span><span class="doccomment">/// A complex number in Cartesian form. |
| /// |
| /// ## Representation and Foreign Function Interface Compatibility |
| /// |
| /// `Complex<T>` is memory layout compatible with an array `[T; 2]`. |
| /// |
| /// Note that `Complex<F>` where F is a floating point type is **only** memory |
| /// layout compatible with C's complex types, **not** necessarily calling |
| /// convention compatible. This means that for FFI you can only pass |
| /// `Complex<F>` behind a pointer, not as a value. |
| /// |
| /// ## Examples |
| /// |
| /// Example of extern function declaration. |
| /// |
| /// ``` |
| /// use num_complex::Complex; |
| /// use std::os::raw::c_int; |
| /// |
| /// extern "C" { |
| /// fn zaxpy_(n: *const c_int, alpha: *const Complex<f64>, |
| /// x: *const Complex<f64>, incx: *const c_int, |
| /// y: *mut Complex<f64>, incy: *const c_int); |
| /// } |
| /// ``` |
| </span><span class="attribute">#[derive(PartialEq, Eq, Copy, Clone, Hash, Debug, Default)] |
| #[repr(C)] |
| </span><span class="kw">pub struct </span>Complex<T> { |
| <span class="doccomment">/// Real portion of the complex number |
| </span><span class="kw">pub </span>re: T, |
| <span class="doccomment">/// Imaginary portion of the complex number |
| </span><span class="kw">pub </span>im: T, |
| } |
| |
| <span class="kw">pub type </span>Complex32 = Complex<f32>; |
| <span class="kw">pub type </span>Complex64 = Complex<f64>; |
| |
| <span class="kw">impl</span><T> Complex<T> { |
| <span class="doccomment">/// Create a new Complex |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub const fn </span>new(re: T, im: T) -> <span class="self">Self </span>{ |
| Complex { re, im } |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num> Complex<T> { |
| <span class="doccomment">/// Returns imaginary unit |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>i() -> <span class="self">Self </span>{ |
| <span class="self">Self</span>::new(T::zero(), T::one()) |
| } |
| |
| <span class="doccomment">/// Returns the square of the norm (since `T` doesn't necessarily |
| /// have a sqrt function), i.e. `re^2 + im^2`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>norm_sqr(<span class="kw-2">&</span><span class="self">self</span>) -> T { |
| <span class="self">self</span>.re.clone() * <span class="self">self</span>.re.clone() + <span class="self">self</span>.im.clone() * <span class="self">self</span>.im.clone() |
| } |
| |
| <span class="doccomment">/// Multiplies `self` by the scalar `t`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>scale(<span class="kw-2">&</span><span class="self">self</span>, t: T) -> <span class="self">Self </span>{ |
| <span class="self">Self</span>::new(<span class="self">self</span>.re.clone() * t.clone(), <span class="self">self</span>.im.clone() * t) |
| } |
| |
| <span class="doccomment">/// Divides `self` by the scalar `t`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>unscale(<span class="kw-2">&</span><span class="self">self</span>, t: T) -> <span class="self">Self </span>{ |
| <span class="self">Self</span>::new(<span class="self">self</span>.re.clone() / t.clone(), <span class="self">self</span>.im.clone() / t) |
| } |
| |
| <span class="doccomment">/// Raises `self` to an unsigned integer power. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>powu(<span class="kw-2">&</span><span class="self">self</span>, exp: u32) -> <span class="self">Self </span>{ |
| Pow::pow(<span class="self">self</span>, exp) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num + Neg<Output = T>> Complex<T> { |
| <span class="doccomment">/// Returns the complex conjugate. i.e. `re - i im` |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>conj(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="self">Self</span>::new(<span class="self">self</span>.re.clone(), -<span class="self">self</span>.im.clone()) |
| } |
| |
| <span class="doccomment">/// Returns `1/self` |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>inv(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="kw">let </span>norm_sqr = <span class="self">self</span>.norm_sqr(); |
| <span class="self">Self</span>::new( |
| <span class="self">self</span>.re.clone() / norm_sqr.clone(), |
| -<span class="self">self</span>.im.clone() / norm_sqr, |
| ) |
| } |
| |
| <span class="doccomment">/// Raises `self` to a signed integer power. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>powi(<span class="kw-2">&</span><span class="self">self</span>, exp: i32) -> <span class="self">Self </span>{ |
| Pow::pow(<span class="self">self</span>, exp) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Signed> Complex<T> { |
| <span class="doccomment">/// Returns the L1 norm `|re| + |im|` -- the [Manhattan distance] from the origin. |
| /// |
| /// [Manhattan distance]: https://en.wikipedia.org/wiki/Taxicab_geometry |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>l1_norm(<span class="kw-2">&</span><span class="self">self</span>) -> T { |
| <span class="self">self</span>.re.abs() + <span class="self">self</span>.im.abs() |
| } |
| } |
| |
| <span class="attribute">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))] |
| </span><span class="kw">impl</span><T: Float> Complex<T> { |
| <span class="doccomment">/// Calculate |self| |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>norm(<span class="self">self</span>) -> T { |
| <span class="self">self</span>.re.hypot(<span class="self">self</span>.im) |
| } |
| <span class="doccomment">/// Calculate the principal Arg of self. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>arg(<span class="self">self</span>) -> T { |
| <span class="self">self</span>.im.atan2(<span class="self">self</span>.re) |
| } |
| <span class="doccomment">/// Convert to polar form (r, theta), such that |
| /// `self = r * exp(i * theta)` |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>to_polar(<span class="self">self</span>) -> (T, T) { |
| (<span class="self">self</span>.norm(), <span class="self">self</span>.arg()) |
| } |
| <span class="doccomment">/// Convert a polar representation into a complex number. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>from_polar(r: T, theta: T) -> <span class="self">Self </span>{ |
| <span class="self">Self</span>::new(r * theta.cos(), r * theta.sin()) |
| } |
| |
| <span class="doccomment">/// Computes `e^(self)`, where `e` is the base of the natural logarithm. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>exp(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: e^(a + bi) = e^a (cos(b) + i*sin(b)) |
| // = from_polar(e^a, b) |
| </span><span class="self">Self</span>::from_polar(<span class="self">self</span>.re.exp(), <span class="self">self</span>.im) |
| } |
| |
| <span class="doccomment">/// Computes the principal value of natural logarithm of `self`. |
| /// |
| /// This function has one branch cut: |
| /// |
| /// * `(-∞, 0]`, continuous from above. |
| /// |
| /// The branch satisfies `-π ≤ arg(ln(z)) ≤ π`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>ln(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: ln(z) = ln|z| + i*arg(z) |
| </span><span class="kw">let </span>(r, theta) = <span class="self">self</span>.to_polar(); |
| <span class="self">Self</span>::new(r.ln(), theta) |
| } |
| |
| <span class="doccomment">/// Computes the principal value of the square root of `self`. |
| /// |
| /// This function has one branch cut: |
| /// |
| /// * `(-∞, 0)`, continuous from above. |
| /// |
| /// The branch satisfies `-π/2 ≤ arg(sqrt(z)) ≤ π/2`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>sqrt(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="kw">if </span><span class="self">self</span>.im.is_zero() { |
| <span class="kw">if </span><span class="self">self</span>.re.is_sign_positive() { |
| <span class="comment">// simple positive real √r, and copy `im` for its sign |
| </span><span class="self">Self</span>::new(<span class="self">self</span>.re.sqrt(), <span class="self">self</span>.im) |
| } <span class="kw">else </span>{ |
| <span class="comment">// √(r e^(iπ)) = √r e^(iπ/2) = i√r |
| // √(r e^(-iπ)) = √r e^(-iπ/2) = -i√r |
| </span><span class="kw">let </span>re = T::zero(); |
| <span class="kw">let </span>im = (-<span class="self">self</span>.re).sqrt(); |
| <span class="kw">if </span><span class="self">self</span>.im.is_sign_positive() { |
| <span class="self">Self</span>::new(re, im) |
| } <span class="kw">else </span>{ |
| <span class="self">Self</span>::new(re, -im) |
| } |
| } |
| } <span class="kw">else if </span><span class="self">self</span>.re.is_zero() { |
| <span class="comment">// √(r e^(iπ/2)) = √r e^(iπ/4) = √(r/2) + i√(r/2) |
| // √(r e^(-iπ/2)) = √r e^(-iπ/4) = √(r/2) - i√(r/2) |
| </span><span class="kw">let </span>one = T::one(); |
| <span class="kw">let </span>two = one + one; |
| <span class="kw">let </span>x = (<span class="self">self</span>.im.abs() / two).sqrt(); |
| <span class="kw">if </span><span class="self">self</span>.im.is_sign_positive() { |
| <span class="self">Self</span>::new(x, x) |
| } <span class="kw">else </span>{ |
| <span class="self">Self</span>::new(x, -x) |
| } |
| } <span class="kw">else </span>{ |
| <span class="comment">// formula: sqrt(r e^(it)) = sqrt(r) e^(it/2) |
| </span><span class="kw">let </span>one = T::one(); |
| <span class="kw">let </span>two = one + one; |
| <span class="kw">let </span>(r, theta) = <span class="self">self</span>.to_polar(); |
| <span class="self">Self</span>::from_polar(r.sqrt(), theta / two) |
| } |
| } |
| |
| <span class="doccomment">/// Computes the principal value of the cube root of `self`. |
| /// |
| /// This function has one branch cut: |
| /// |
| /// * `(-∞, 0)`, continuous from above. |
| /// |
| /// The branch satisfies `-π/3 ≤ arg(cbrt(z)) ≤ π/3`. |
| /// |
| /// Note that this does not match the usual result for the cube root of |
| /// negative real numbers. For example, the real cube root of `-8` is `-2`, |
| /// but the principal complex cube root of `-8` is `1 + i√3`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>cbrt(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="kw">if </span><span class="self">self</span>.im.is_zero() { |
| <span class="kw">if </span><span class="self">self</span>.re.is_sign_positive() { |
| <span class="comment">// simple positive real ∛r, and copy `im` for its sign |
| </span><span class="self">Self</span>::new(<span class="self">self</span>.re.cbrt(), <span class="self">self</span>.im) |
| } <span class="kw">else </span>{ |
| <span class="comment">// ∛(r e^(iπ)) = ∛r e^(iπ/3) = ∛r/2 + i∛r√3/2 |
| // ∛(r e^(-iπ)) = ∛r e^(-iπ/3) = ∛r/2 - i∛r√3/2 |
| </span><span class="kw">let </span>one = T::one(); |
| <span class="kw">let </span>two = one + one; |
| <span class="kw">let </span>three = two + one; |
| <span class="kw">let </span>re = (-<span class="self">self</span>.re).cbrt() / two; |
| <span class="kw">let </span>im = three.sqrt() * re; |
| <span class="kw">if </span><span class="self">self</span>.im.is_sign_positive() { |
| <span class="self">Self</span>::new(re, im) |
| } <span class="kw">else </span>{ |
| <span class="self">Self</span>::new(re, -im) |
| } |
| } |
| } <span class="kw">else if </span><span class="self">self</span>.re.is_zero() { |
| <span class="comment">// ∛(r e^(iπ/2)) = ∛r e^(iπ/6) = ∛r√3/2 + i∛r/2 |
| // ∛(r e^(-iπ/2)) = ∛r e^(-iπ/6) = ∛r√3/2 - i∛r/2 |
| </span><span class="kw">let </span>one = T::one(); |
| <span class="kw">let </span>two = one + one; |
| <span class="kw">let </span>three = two + one; |
| <span class="kw">let </span>im = <span class="self">self</span>.im.abs().cbrt() / two; |
| <span class="kw">let </span>re = three.sqrt() * im; |
| <span class="kw">if </span><span class="self">self</span>.im.is_sign_positive() { |
| <span class="self">Self</span>::new(re, im) |
| } <span class="kw">else </span>{ |
| <span class="self">Self</span>::new(re, -im) |
| } |
| } <span class="kw">else </span>{ |
| <span class="comment">// formula: cbrt(r e^(it)) = cbrt(r) e^(it/3) |
| </span><span class="kw">let </span>one = T::one(); |
| <span class="kw">let </span>three = one + one + one; |
| <span class="kw">let </span>(r, theta) = <span class="self">self</span>.to_polar(); |
| <span class="self">Self</span>::from_polar(r.cbrt(), theta / three) |
| } |
| } |
| |
| <span class="doccomment">/// Raises `self` to a floating point power. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>powf(<span class="self">self</span>, exp: T) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: x^y = (ρ e^(i θ))^y = ρ^y e^(i θ y) |
| // = from_polar(ρ^y, θ y) |
| </span><span class="kw">let </span>(r, theta) = <span class="self">self</span>.to_polar(); |
| <span class="self">Self</span>::from_polar(r.powf(exp), theta * exp) |
| } |
| |
| <span class="doccomment">/// Returns the logarithm of `self` with respect to an arbitrary base. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>log(<span class="self">self</span>, base: T) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: log_y(x) = log_y(ρ e^(i θ)) |
| // = log_y(ρ) + log_y(e^(i θ)) = log_y(ρ) + ln(e^(i θ)) / ln(y) |
| // = log_y(ρ) + i θ / ln(y) |
| </span><span class="kw">let </span>(r, theta) = <span class="self">self</span>.to_polar(); |
| <span class="self">Self</span>::new(r.log(base), theta / base.ln()) |
| } |
| |
| <span class="doccomment">/// Raises `self` to a complex power. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>powc(<span class="self">self</span>, exp: <span class="self">Self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: x^y = (a + i b)^(c + i d) |
| // = (ρ e^(i θ))^c (ρ e^(i θ))^(i d) |
| // where ρ=|x| and θ=arg(x) |
| // = ρ^c e^(−d θ) e^(i c θ) ρ^(i d) |
| // = p^c e^(−d θ) (cos(c θ) |
| // + i sin(c θ)) (cos(d ln(ρ)) + i sin(d ln(ρ))) |
| // = p^c e^(−d θ) ( |
| // cos(c θ) cos(d ln(ρ)) − sin(c θ) sin(d ln(ρ)) |
| // + i(cos(c θ) sin(d ln(ρ)) + sin(c θ) cos(d ln(ρ)))) |
| // = p^c e^(−d θ) (cos(c θ + d ln(ρ)) + i sin(c θ + d ln(ρ))) |
| // = from_polar(p^c e^(−d θ), c θ + d ln(ρ)) |
| </span><span class="kw">let </span>(r, theta) = <span class="self">self</span>.to_polar(); |
| <span class="self">Self</span>::from_polar( |
| r.powf(exp.re) * (-exp.im * theta).exp(), |
| exp.re * theta + exp.im * r.ln(), |
| ) |
| } |
| |
| <span class="doccomment">/// Raises a floating point number to the complex power `self`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>expf(<span class="self">self</span>, base: T) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: x^(a+bi) = x^a x^bi = x^a e^(b ln(x) i) |
| // = from_polar(x^a, b ln(x)) |
| </span><span class="self">Self</span>::from_polar(base.powf(<span class="self">self</span>.re), <span class="self">self</span>.im * base.ln()) |
| } |
| |
| <span class="doccomment">/// Computes the sine of `self`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>sin(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: sin(a + bi) = sin(a)cosh(b) + i*cos(a)sinh(b) |
| </span><span class="self">Self</span>::new( |
| <span class="self">self</span>.re.sin() * <span class="self">self</span>.im.cosh(), |
| <span class="self">self</span>.re.cos() * <span class="self">self</span>.im.sinh(), |
| ) |
| } |
| |
| <span class="doccomment">/// Computes the cosine of `self`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>cos(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: cos(a + bi) = cos(a)cosh(b) - i*sin(a)sinh(b) |
| </span><span class="self">Self</span>::new( |
| <span class="self">self</span>.re.cos() * <span class="self">self</span>.im.cosh(), |
| -<span class="self">self</span>.re.sin() * <span class="self">self</span>.im.sinh(), |
| ) |
| } |
| |
| <span class="doccomment">/// Computes the tangent of `self`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>tan(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: tan(a + bi) = (sin(2a) + i*sinh(2b))/(cos(2a) + cosh(2b)) |
| </span><span class="kw">let </span>(two_re, two_im) = (<span class="self">self</span>.re + <span class="self">self</span>.re, <span class="self">self</span>.im + <span class="self">self</span>.im); |
| <span class="self">Self</span>::new(two_re.sin(), two_im.sinh()).unscale(two_re.cos() + two_im.cosh()) |
| } |
| |
| <span class="doccomment">/// Computes the principal value of the inverse sine of `self`. |
| /// |
| /// This function has two branch cuts: |
| /// |
| /// * `(-∞, -1)`, continuous from above. |
| /// * `(1, ∞)`, continuous from below. |
| /// |
| /// The branch satisfies `-π/2 ≤ Re(asin(z)) ≤ π/2`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>asin(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: arcsin(z) = -i ln(sqrt(1-z^2) + iz) |
| </span><span class="kw">let </span>i = <span class="self">Self</span>::i(); |
| -i * ((<span class="self">Self</span>::one() - <span class="self">self </span>* <span class="self">self</span>).sqrt() + i * <span class="self">self</span>).ln() |
| } |
| |
| <span class="doccomment">/// Computes the principal value of the inverse cosine of `self`. |
| /// |
| /// This function has two branch cuts: |
| /// |
| /// * `(-∞, -1)`, continuous from above. |
| /// * `(1, ∞)`, continuous from below. |
| /// |
| /// The branch satisfies `0 ≤ Re(acos(z)) ≤ π`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>acos(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: arccos(z) = -i ln(i sqrt(1-z^2) + z) |
| </span><span class="kw">let </span>i = <span class="self">Self</span>::i(); |
| -i * (i * (<span class="self">Self</span>::one() - <span class="self">self </span>* <span class="self">self</span>).sqrt() + <span class="self">self</span>).ln() |
| } |
| |
| <span class="doccomment">/// Computes the principal value of the inverse tangent of `self`. |
| /// |
| /// This function has two branch cuts: |
| /// |
| /// * `(-∞i, -i]`, continuous from the left. |
| /// * `[i, ∞i)`, continuous from the right. |
| /// |
| /// The branch satisfies `-π/2 ≤ Re(atan(z)) ≤ π/2`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>atan(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: arctan(z) = (ln(1+iz) - ln(1-iz))/(2i) |
| </span><span class="kw">let </span>i = <span class="self">Self</span>::i(); |
| <span class="kw">let </span>one = <span class="self">Self</span>::one(); |
| <span class="kw">let </span>two = one + one; |
| <span class="kw">if </span><span class="self">self </span>== i { |
| <span class="kw">return </span><span class="self">Self</span>::new(T::zero(), T::infinity()); |
| } <span class="kw">else if </span><span class="self">self </span>== -i { |
| <span class="kw">return </span><span class="self">Self</span>::new(T::zero(), -T::infinity()); |
| } |
| ((one + i * <span class="self">self</span>).ln() - (one - i * <span class="self">self</span>).ln()) / (two * i) |
| } |
| |
| <span class="doccomment">/// Computes the hyperbolic sine of `self`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>sinh(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: sinh(a + bi) = sinh(a)cos(b) + i*cosh(a)sin(b) |
| </span><span class="self">Self</span>::new( |
| <span class="self">self</span>.re.sinh() * <span class="self">self</span>.im.cos(), |
| <span class="self">self</span>.re.cosh() * <span class="self">self</span>.im.sin(), |
| ) |
| } |
| |
| <span class="doccomment">/// Computes the hyperbolic cosine of `self`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>cosh(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: cosh(a + bi) = cosh(a)cos(b) + i*sinh(a)sin(b) |
| </span><span class="self">Self</span>::new( |
| <span class="self">self</span>.re.cosh() * <span class="self">self</span>.im.cos(), |
| <span class="self">self</span>.re.sinh() * <span class="self">self</span>.im.sin(), |
| ) |
| } |
| |
| <span class="doccomment">/// Computes the hyperbolic tangent of `self`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>tanh(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: tanh(a + bi) = (sinh(2a) + i*sin(2b))/(cosh(2a) + cos(2b)) |
| </span><span class="kw">let </span>(two_re, two_im) = (<span class="self">self</span>.re + <span class="self">self</span>.re, <span class="self">self</span>.im + <span class="self">self</span>.im); |
| <span class="self">Self</span>::new(two_re.sinh(), two_im.sin()).unscale(two_re.cosh() + two_im.cos()) |
| } |
| |
| <span class="doccomment">/// Computes the principal value of inverse hyperbolic sine of `self`. |
| /// |
| /// This function has two branch cuts: |
| /// |
| /// * `(-∞i, -i)`, continuous from the left. |
| /// * `(i, ∞i)`, continuous from the right. |
| /// |
| /// The branch satisfies `-π/2 ≤ Im(asinh(z)) ≤ π/2`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>asinh(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: arcsinh(z) = ln(z + sqrt(1+z^2)) |
| </span><span class="kw">let </span>one = <span class="self">Self</span>::one(); |
| (<span class="self">self </span>+ (one + <span class="self">self </span>* <span class="self">self</span>).sqrt()).ln() |
| } |
| |
| <span class="doccomment">/// Computes the principal value of inverse hyperbolic cosine of `self`. |
| /// |
| /// This function has one branch cut: |
| /// |
| /// * `(-∞, 1)`, continuous from above. |
| /// |
| /// The branch satisfies `-π ≤ Im(acosh(z)) ≤ π` and `0 ≤ Re(acosh(z)) < ∞`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>acosh(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: arccosh(z) = 2 ln(sqrt((z+1)/2) + sqrt((z-1)/2)) |
| </span><span class="kw">let </span>one = <span class="self">Self</span>::one(); |
| <span class="kw">let </span>two = one + one; |
| two * (((<span class="self">self </span>+ one) / two).sqrt() + ((<span class="self">self </span>- one) / two).sqrt()).ln() |
| } |
| |
| <span class="doccomment">/// Computes the principal value of inverse hyperbolic tangent of `self`. |
| /// |
| /// This function has two branch cuts: |
| /// |
| /// * `(-∞, -1]`, continuous from above. |
| /// * `[1, ∞)`, continuous from below. |
| /// |
| /// The branch satisfies `-π/2 ≤ Im(atanh(z)) ≤ π/2`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>atanh(<span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="comment">// formula: arctanh(z) = (ln(1+z) - ln(1-z))/2 |
| </span><span class="kw">let </span>one = <span class="self">Self</span>::one(); |
| <span class="kw">let </span>two = one + one; |
| <span class="kw">if </span><span class="self">self </span>== one { |
| <span class="kw">return </span><span class="self">Self</span>::new(T::infinity(), T::zero()); |
| } <span class="kw">else if </span><span class="self">self </span>== -one { |
| <span class="kw">return </span><span class="self">Self</span>::new(-T::infinity(), T::zero()); |
| } |
| ((one + <span class="self">self</span>).ln() - (one - <span class="self">self</span>).ln()) / two |
| } |
| |
| <span class="doccomment">/// Returns `1/self` using floating-point operations. |
| /// |
| /// This may be more accurate than the generic `self.inv()` in cases |
| /// where `self.norm_sqr()` would overflow to ∞ or underflow to 0. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_complex::Complex64; |
| /// let c = Complex64::new(1e300, 1e300); |
| /// |
| /// // The generic `inv()` will overflow. |
| /// assert!(!c.inv().is_normal()); |
| /// |
| /// // But we can do better for `Float` types. |
| /// let inv = c.finv(); |
| /// assert!(inv.is_normal()); |
| /// println!("{:e}", inv); |
| /// |
| /// let expected = Complex64::new(5e-301, -5e-301); |
| /// assert!((inv - expected).norm() < 1e-315); |
| /// ``` |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>finv(<span class="self">self</span>) -> Complex<T> { |
| <span class="kw">let </span>norm = <span class="self">self</span>.norm(); |
| <span class="self">self</span>.conj() / norm / norm |
| } |
| |
| <span class="doccomment">/// Returns `self/other` using floating-point operations. |
| /// |
| /// This may be more accurate than the generic `Div` implementation in cases |
| /// where `other.norm_sqr()` would overflow to ∞ or underflow to 0. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_complex::Complex64; |
| /// let a = Complex64::new(2.0, 3.0); |
| /// let b = Complex64::new(1e300, 1e300); |
| /// |
| /// // Generic division will overflow. |
| /// assert!(!(a / b).is_normal()); |
| /// |
| /// // But we can do better for `Float` types. |
| /// let quotient = a.fdiv(b); |
| /// assert!(quotient.is_normal()); |
| /// println!("{:e}", quotient); |
| /// |
| /// let expected = Complex64::new(2.5e-300, 5e-301); |
| /// assert!((quotient - expected).norm() < 1e-315); |
| /// ``` |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>fdiv(<span class="self">self</span>, other: Complex<T>) -> Complex<T> { |
| <span class="self">self </span>* other.finv() |
| } |
| } |
| |
| <span class="kw">impl</span><T: FloatCore> Complex<T> { |
| <span class="doccomment">/// Checks if the given complex number is NaN |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>is_nan(<span class="self">self</span>) -> bool { |
| <span class="self">self</span>.re.is_nan() || <span class="self">self</span>.im.is_nan() |
| } |
| |
| <span class="doccomment">/// Checks if the given complex number is infinite |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>is_infinite(<span class="self">self</span>) -> bool { |
| !<span class="self">self</span>.is_nan() && (<span class="self">self</span>.re.is_infinite() || <span class="self">self</span>.im.is_infinite()) |
| } |
| |
| <span class="doccomment">/// Checks if the given complex number is finite |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>is_finite(<span class="self">self</span>) -> bool { |
| <span class="self">self</span>.re.is_finite() && <span class="self">self</span>.im.is_finite() |
| } |
| |
| <span class="doccomment">/// Checks if the given complex number is normal |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>is_normal(<span class="self">self</span>) -> bool { |
| <span class="self">self</span>.re.is_normal() && <span class="self">self</span>.im.is_normal() |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num> From<T> <span class="kw">for </span>Complex<T> { |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>from(re: T) -> <span class="self">Self </span>{ |
| <span class="self">Self</span>::new(re, T::zero()) |
| } |
| } |
| |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + Num> From<<span class="kw-2">&</span><span class="lifetime">'a </span>T> <span class="kw">for </span>Complex<T> { |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>from(re: <span class="kw-2">&</span>T) -> <span class="self">Self </span>{ |
| From::from(re.clone()) |
| } |
| } |
| |
| <span class="macro">macro_rules! </span>forward_ref_ref_binop { |
| (<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => { |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, <span class="lifetime">'b</span>, T: Clone + Num> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'b </span>Complex<T>> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: <span class="kw-2">&</span>Complex<T>) -> <span class="self">Self</span>::Output { |
| <span class="self">self</span>.clone().<span class="macro-nonterminal">$method</span>(other.clone()) |
| } |
| } |
| }; |
| } |
| |
| <span class="macro">macro_rules! </span>forward_ref_val_binop { |
| (<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => { |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + Num> <span class="macro-nonterminal">$imp</span><Complex<T>> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: Complex<T>) -> <span class="self">Self</span>::Output { |
| <span class="self">self</span>.clone().<span class="macro-nonterminal">$method</span>(other) |
| } |
| } |
| }; |
| } |
| |
| <span class="macro">macro_rules! </span>forward_val_ref_binop { |
| (<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => { |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + Num> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T>> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: <span class="kw-2">&</span>Complex<T>) -> <span class="self">Self</span>::Output { |
| <span class="self">self</span>.<span class="macro-nonterminal">$method</span>(other.clone()) |
| } |
| } |
| }; |
| } |
| |
| <span class="macro">macro_rules! </span>forward_all_binop { |
| (<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => { |
| <span class="macro">forward_ref_ref_binop!</span>(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>, <span class="macro-nonterminal">$method</span>); |
| <span class="macro">forward_ref_val_binop!</span>(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>, <span class="macro-nonterminal">$method</span>); |
| <span class="macro">forward_val_ref_binop!</span>(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>, <span class="macro-nonterminal">$method</span>); |
| }; |
| } |
| |
| <span class="comment">// arithmetic |
| </span><span class="macro">forward_all_binop!</span>(<span class="kw">impl </span>Add, add); |
| |
| <span class="comment">// (a + i b) + (c + i d) == (a + c) + i (b + d) |
| </span><span class="kw">impl</span><T: Clone + Num> Add<Complex<T>> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = <span class="self">Self</span>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>add(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self</span>.re + other.re, <span class="self">self</span>.im + other.im) |
| } |
| } |
| |
| <span class="macro">forward_all_binop!</span>(<span class="kw">impl </span>Sub, sub); |
| |
| <span class="comment">// (a + i b) - (c + i d) == (a - c) + i (b - d) |
| </span><span class="kw">impl</span><T: Clone + Num> Sub<Complex<T>> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = <span class="self">Self</span>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>sub(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self</span>.re - other.re, <span class="self">self</span>.im - other.im) |
| } |
| } |
| |
| <span class="macro">forward_all_binop!</span>(<span class="kw">impl </span>Mul, mul); |
| |
| <span class="comment">// (a + i b) * (c + i d) == (a*c - b*d) + i (a*d + b*c) |
| </span><span class="kw">impl</span><T: Clone + Num> Mul<Complex<T>> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = <span class="self">Self</span>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>mul(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>::Output { |
| <span class="kw">let </span>re = <span class="self">self</span>.re.clone() * other.re.clone() - <span class="self">self</span>.im.clone() * other.im.clone(); |
| <span class="kw">let </span>im = <span class="self">self</span>.re * other.im + <span class="self">self</span>.im * other.re; |
| <span class="self">Self</span>::Output::new(re, im) |
| } |
| } |
| |
| <span class="comment">// (a + i b) * (c + i d) + (e + i f) == ((a*c + e) - b*d) + i (a*d + (b*c + f)) |
| </span><span class="kw">impl</span><T: Clone + Num + MulAdd<Output = T>> MulAdd<Complex<T>> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>mul_add(<span class="self">self</span>, other: Complex<T>, add: Complex<T>) -> Complex<T> { |
| <span class="kw">let </span>re = <span class="self">self</span>.re.clone().mul_add(other.re.clone(), add.re) |
| - (<span class="self">self</span>.im.clone() * other.im.clone()); <span class="comment">// FIXME: use mulsub when available in rust |
| </span><span class="kw">let </span>im = <span class="self">self</span>.re.mul_add(other.im, <span class="self">self</span>.im.mul_add(other.re, add.im)); |
| Complex::new(re, im) |
| } |
| } |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, <span class="lifetime">'b</span>, T: Clone + Num + MulAdd<Output = T>> MulAdd<<span class="kw-2">&</span><span class="lifetime">'b </span>Complex<T>> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>mul_add(<span class="self">self</span>, other: <span class="kw-2">&</span>Complex<T>, add: <span class="kw-2">&</span>Complex<T>) -> Complex<T> { |
| <span class="self">self</span>.clone().mul_add(other.clone(), add.clone()) |
| } |
| } |
| |
| <span class="macro">forward_all_binop!</span>(<span class="kw">impl </span>Div, div); |
| |
| <span class="comment">// (a + i b) / (c + i d) == [(a + i b) * (c - i d)] / (c*c + d*d) |
| // == [(a*c + b*d) / (c*c + d*d)] + i [(b*c - a*d) / (c*c + d*d)] |
| </span><span class="kw">impl</span><T: Clone + Num> Div<Complex<T>> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = <span class="self">Self</span>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>div(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>::Output { |
| <span class="kw">let </span>norm_sqr = other.norm_sqr(); |
| <span class="kw">let </span>re = <span class="self">self</span>.re.clone() * other.re.clone() + <span class="self">self</span>.im.clone() * other.im.clone(); |
| <span class="kw">let </span>im = <span class="self">self</span>.im * other.re - <span class="self">self</span>.re * other.im; |
| <span class="self">Self</span>::Output::new(re / norm_sqr.clone(), im / norm_sqr) |
| } |
| } |
| |
| <span class="macro">forward_all_binop!</span>(<span class="kw">impl </span>Rem, rem); |
| |
| <span class="kw">impl</span><T: Clone + Num> Complex<T> { |
| <span class="doccomment">/// Find the gaussian integer corresponding to the true ratio rounded towards zero. |
| </span><span class="kw">fn </span>div_trunc(<span class="kw-2">&</span><span class="self">self</span>, divisor: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{ |
| <span class="kw">let </span>Complex { re, im } = <span class="self">self </span>/ divisor; |
| Complex::new(re.clone() - re % T::one(), im.clone() - im % T::one()) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num> Rem<Complex<T>> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = <span class="self">Self</span>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>rem(<span class="self">self</span>, modulus: <span class="self">Self</span>) -> <span class="self">Self</span>::Output { |
| <span class="kw">let </span>gaussian = <span class="self">self</span>.div_trunc(<span class="kw-2">&</span>modulus); |
| <span class="self">self </span>- modulus * gaussian |
| } |
| } |
| |
| <span class="comment">// Op Assign |
| |
| </span><span class="kw">mod </span>opassign { |
| <span class="kw">use </span>core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign}; |
| |
| <span class="kw">use </span>num_traits::{MulAddAssign, NumAssign}; |
| |
| <span class="kw">use </span><span class="kw">crate</span>::Complex; |
| |
| <span class="kw">impl</span><T: Clone + NumAssign> AddAssign <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>add_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="self">Self</span>) { |
| <span class="self">self</span>.re += other.re; |
| <span class="self">self</span>.im += other.im; |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + NumAssign> SubAssign <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>sub_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="self">Self</span>) { |
| <span class="self">self</span>.re -= other.re; |
| <span class="self">self</span>.im -= other.im; |
| } |
| } |
| |
| <span class="comment">// (a + i b) * (c + i d) == (a*c - b*d) + i (a*d + b*c) |
| </span><span class="kw">impl</span><T: Clone + NumAssign> MulAssign <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>mul_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="self">Self</span>) { |
| <span class="kw">let </span>a = <span class="self">self</span>.re.clone(); |
| |
| <span class="self">self</span>.re <span class="kw-2">*</span>= other.re.clone(); |
| <span class="self">self</span>.re -= <span class="self">self</span>.im.clone() * other.im.clone(); |
| |
| <span class="self">self</span>.im <span class="kw-2">*</span>= other.re; |
| <span class="self">self</span>.im += a * other.im; |
| } |
| } |
| |
| <span class="comment">// (a + i b) * (c + i d) + (e + i f) == ((a*c + e) - b*d) + i (b*c + (a*d + f)) |
| </span><span class="kw">impl</span><T: Clone + NumAssign + MulAddAssign> MulAddAssign <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>mul_add_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: Complex<T>, add: Complex<T>) { |
| <span class="kw">let </span>a = <span class="self">self</span>.re.clone(); |
| |
| <span class="self">self</span>.re.mul_add_assign(other.re.clone(), add.re); <span class="comment">// (a*c + e) |
| </span><span class="self">self</span>.re -= <span class="self">self</span>.im.clone() * other.im.clone(); <span class="comment">// ((a*c + e) - b*d) |
| |
| </span><span class="kw">let </span><span class="kw-2">mut </span>adf = a; |
| adf.mul_add_assign(other.im, add.im); <span class="comment">// (a*d + f) |
| </span><span class="self">self</span>.im.mul_add_assign(other.re, adf); <span class="comment">// (b*c + (a*d + f)) |
| </span>} |
| } |
| |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, <span class="lifetime">'b</span>, T: Clone + NumAssign + MulAddAssign> MulAddAssign<<span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T>, <span class="kw-2">&</span><span class="lifetime">'b </span>Complex<T>> |
| <span class="kw">for </span>Complex<T> |
| { |
| <span class="kw">fn </span>mul_add_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="kw-2">&</span>Complex<T>, add: <span class="kw-2">&</span>Complex<T>) { |
| <span class="self">self</span>.mul_add_assign(other.clone(), add.clone()); |
| } |
| } |
| |
| <span class="comment">// (a + i b) / (c + i d) == [(a + i b) * (c - i d)] / (c*c + d*d) |
| // == [(a*c + b*d) / (c*c + d*d)] + i [(b*c - a*d) / (c*c + d*d)] |
| </span><span class="kw">impl</span><T: Clone + NumAssign> DivAssign <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>div_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="self">Self</span>) { |
| <span class="kw">let </span>a = <span class="self">self</span>.re.clone(); |
| <span class="kw">let </span>norm_sqr = other.norm_sqr(); |
| |
| <span class="self">self</span>.re <span class="kw-2">*</span>= other.re.clone(); |
| <span class="self">self</span>.re += <span class="self">self</span>.im.clone() * other.im.clone(); |
| <span class="self">self</span>.re /= norm_sqr.clone(); |
| |
| <span class="self">self</span>.im <span class="kw-2">*</span>= other.re; |
| <span class="self">self</span>.im -= a * other.im; |
| <span class="self">self</span>.im /= norm_sqr; |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + NumAssign> RemAssign <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>rem_assign(<span class="kw-2">&mut </span><span class="self">self</span>, modulus: <span class="self">Self</span>) { |
| <span class="kw">let </span>gaussian = <span class="self">self</span>.div_trunc(<span class="kw-2">&</span>modulus); |
| <span class="kw-2">*</span><span class="self">self </span>-= modulus * gaussian; |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + NumAssign> AddAssign<T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>add_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: T) { |
| <span class="self">self</span>.re += other; |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + NumAssign> SubAssign<T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>sub_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: T) { |
| <span class="self">self</span>.re -= other; |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + NumAssign> MulAssign<T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>mul_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: T) { |
| <span class="self">self</span>.re <span class="kw-2">*</span>= other.clone(); |
| <span class="self">self</span>.im <span class="kw-2">*</span>= other; |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + NumAssign> DivAssign<T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>div_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: T) { |
| <span class="self">self</span>.re /= other.clone(); |
| <span class="self">self</span>.im /= other; |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + NumAssign> RemAssign<T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>rem_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: T) { |
| <span class="self">self</span>.re %= other.clone(); |
| <span class="self">self</span>.im %= other; |
| } |
| } |
| |
| <span class="macro">macro_rules! </span>forward_op_assign { |
| (<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => { |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + NumAssign> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T>> <span class="kw">for </span>Complex<T> { |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) { |
| <span class="self">self</span>.<span class="macro-nonterminal">$method</span>(other.clone()) |
| } |
| } |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + NumAssign> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>T> <span class="kw">for </span>Complex<T> { |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="kw-2">&</span>T) { |
| <span class="self">self</span>.<span class="macro-nonterminal">$method</span>(other.clone()) |
| } |
| } |
| }; |
| } |
| |
| <span class="macro">forward_op_assign!</span>(<span class="kw">impl </span>AddAssign, add_assign); |
| <span class="macro">forward_op_assign!</span>(<span class="kw">impl </span>SubAssign, sub_assign); |
| <span class="macro">forward_op_assign!</span>(<span class="kw">impl </span>MulAssign, mul_assign); |
| <span class="macro">forward_op_assign!</span>(<span class="kw">impl </span>DivAssign, div_assign); |
| <span class="macro">forward_op_assign!</span>(<span class="kw">impl </span>RemAssign, rem_assign); |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num + Neg<Output = T>> Neg <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = <span class="self">Self</span>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>neg(<span class="self">self</span>) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(-<span class="self">self</span>.re, -<span class="self">self</span>.im) |
| } |
| } |
| |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + Num + Neg<Output = T>> Neg <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>neg(<span class="self">self</span>) -> <span class="self">Self</span>::Output { |
| -<span class="self">self</span>.clone() |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num + Neg<Output = T>> Inv <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = <span class="self">Self</span>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>inv(<span class="self">self</span>) -> <span class="self">Self</span>::Output { |
| (<span class="kw-2">&</span><span class="self">self</span>).inv() |
| } |
| } |
| |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + Num + Neg<Output = T>> Inv <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>inv(<span class="self">self</span>) -> <span class="self">Self</span>::Output { |
| <span class="self">self</span>.inv() |
| } |
| } |
| |
| <span class="macro">macro_rules! </span>real_arithmetic { |
| (@forward <span class="macro-nonterminal">$imp</span>:ident::<span class="macro-nonterminal">$method</span>:ident <span class="kw">for </span>$(<span class="macro-nonterminal">$real</span>:ident),<span class="kw-2">*</span>) => ( |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + Num> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: <span class="kw-2">&</span>T) -> <span class="self">Self</span>::Output { |
| <span class="self">self</span>.<span class="macro-nonterminal">$method</span>(other.clone()) |
| } |
| } |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + Num> <span class="macro-nonterminal">$imp</span><T> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: T) -> <span class="self">Self</span>::Output { |
| <span class="self">self</span>.clone().<span class="macro-nonterminal">$method</span>(other) |
| } |
| } |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, <span class="lifetime">'b</span>, T: Clone + Num> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>T> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'b </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: <span class="kw-2">&</span>T) -> <span class="self">Self</span>::Output { |
| <span class="self">self</span>.clone().<span class="macro-nonterminal">$method</span>(other.clone()) |
| } |
| } |
| $( |
| <span class="kw">impl</span><<span class="lifetime">'a</span>> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>Complex<<span class="macro-nonterminal">$real</span>>> <span class="kw">for </span><span class="macro-nonterminal">$real </span>{ |
| <span class="kw">type </span>Output = Complex<<span class="macro-nonterminal">$real</span>>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: <span class="kw-2">&</span>Complex<<span class="macro-nonterminal">$real</span>>) -> Complex<<span class="macro-nonterminal">$real</span>> { |
| <span class="self">self</span>.<span class="macro-nonterminal">$method</span>(other.clone()) |
| } |
| } |
| <span class="kw">impl</span><<span class="lifetime">'a</span>> <span class="macro-nonterminal">$imp</span><Complex<<span class="macro-nonterminal">$real</span>>> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span><span class="macro-nonterminal">$real </span>{ |
| <span class="kw">type </span>Output = Complex<<span class="macro-nonterminal">$real</span>>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: Complex<<span class="macro-nonterminal">$real</span>>) -> Complex<<span class="macro-nonterminal">$real</span>> { |
| <span class="self">self</span>.clone().<span class="macro-nonterminal">$method</span>(other) |
| } |
| } |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, <span class="lifetime">'b</span>> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>Complex<<span class="macro-nonterminal">$real</span>>> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'b </span><span class="macro-nonterminal">$real </span>{ |
| <span class="kw">type </span>Output = Complex<<span class="macro-nonterminal">$real</span>>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: <span class="kw-2">&</span>Complex<<span class="macro-nonterminal">$real</span>>) -> Complex<<span class="macro-nonterminal">$real</span>> { |
| <span class="self">self</span>.clone().<span class="macro-nonterminal">$method</span>(other.clone()) |
| } |
| } |
| )* |
| ); |
| ($(<span class="macro-nonterminal">$real</span>:ident),<span class="kw-2">*</span>) => ( |
| <span class="macro">real_arithmetic!</span>(@forward Add::add <span class="kw">for </span>$(<span class="macro-nonterminal">$real</span>),<span class="kw-2">*</span>); |
| <span class="macro">real_arithmetic!</span>(@forward Sub::sub <span class="kw">for </span>$(<span class="macro-nonterminal">$real</span>),<span class="kw-2">*</span>); |
| <span class="macro">real_arithmetic!</span>(@forward Mul::mul <span class="kw">for </span>$(<span class="macro-nonterminal">$real</span>),<span class="kw-2">*</span>); |
| <span class="macro">real_arithmetic!</span>(@forward Div::div <span class="kw">for </span>$(<span class="macro-nonterminal">$real</span>),<span class="kw-2">*</span>); |
| <span class="macro">real_arithmetic!</span>(@forward Rem::rem <span class="kw">for </span>$(<span class="macro-nonterminal">$real</span>),<span class="kw-2">*</span>); |
| |
| $( |
| <span class="kw">impl </span>Add<Complex<<span class="macro-nonterminal">$real</span>>> <span class="kw">for </span><span class="macro-nonterminal">$real </span>{ |
| <span class="kw">type </span>Output = Complex<<span class="macro-nonterminal">$real</span>>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>add(<span class="self">self</span>, other: Complex<<span class="macro-nonterminal">$real</span>>) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self </span>+ other.re, other.im) |
| } |
| } |
| |
| <span class="kw">impl </span>Sub<Complex<<span class="macro-nonterminal">$real</span>>> <span class="kw">for </span><span class="macro-nonterminal">$real </span>{ |
| <span class="kw">type </span>Output = Complex<<span class="macro-nonterminal">$real</span>>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>sub(<span class="self">self</span>, other: Complex<<span class="macro-nonterminal">$real</span>>) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self </span>- other.re, <span class="macro-nonterminal">$real::zero</span>() - other.im) |
| } |
| } |
| |
| <span class="kw">impl </span>Mul<Complex<<span class="macro-nonterminal">$real</span>>> <span class="kw">for </span><span class="macro-nonterminal">$real </span>{ |
| <span class="kw">type </span>Output = Complex<<span class="macro-nonterminal">$real</span>>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>mul(<span class="self">self</span>, other: Complex<<span class="macro-nonterminal">$real</span>>) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self </span>* other.re, <span class="self">self </span>* other.im) |
| } |
| } |
| |
| <span class="kw">impl </span>Div<Complex<<span class="macro-nonterminal">$real</span>>> <span class="kw">for </span><span class="macro-nonterminal">$real </span>{ |
| <span class="kw">type </span>Output = Complex<<span class="macro-nonterminal">$real</span>>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>div(<span class="self">self</span>, other: Complex<<span class="macro-nonterminal">$real</span>>) -> <span class="self">Self</span>::Output { |
| <span class="comment">// a / (c + i d) == [a * (c - i d)] / (c*c + d*d) |
| </span><span class="kw">let </span>norm_sqr = other.norm_sqr(); |
| <span class="self">Self</span>::Output::new(<span class="self">self </span>* other.re / norm_sqr.clone(), |
| <span class="macro-nonterminal">$real::zero</span>() - <span class="self">self </span>* other.im / norm_sqr) |
| } |
| } |
| |
| <span class="kw">impl </span>Rem<Complex<<span class="macro-nonterminal">$real</span>>> <span class="kw">for </span><span class="macro-nonterminal">$real </span>{ |
| <span class="kw">type </span>Output = Complex<<span class="macro-nonterminal">$real</span>>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>rem(<span class="self">self</span>, other: Complex<<span class="macro-nonterminal">$real</span>>) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self</span>, <span class="self">Self</span>::zero()) % other |
| } |
| } |
| )* |
| ); |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num> Add<T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>add(<span class="self">self</span>, other: T) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self</span>.re + other, <span class="self">self</span>.im) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num> Sub<T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>sub(<span class="self">self</span>, other: T) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self</span>.re - other, <span class="self">self</span>.im) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num> Mul<T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>mul(<span class="self">self</span>, other: T) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self</span>.re * other.clone(), <span class="self">self</span>.im * other) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num> Div<T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = <span class="self">Self</span>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>div(<span class="self">self</span>, other: T) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self</span>.re / other.clone(), <span class="self">self</span>.im / other) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num> Rem<T> <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>Output = Complex<T>; |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>rem(<span class="self">self</span>, other: T) -> <span class="self">Self</span>::Output { |
| <span class="self">Self</span>::Output::new(<span class="self">self</span>.re % other.clone(), <span class="self">self</span>.im % other) |
| } |
| } |
| |
| <span class="macro">real_arithmetic!</span>(usize, u8, u16, u32, u64, u128, isize, i8, i16, i32, i64, i128, f32, f64); |
| |
| <span class="comment">// constants |
| </span><span class="kw">impl</span><T: Clone + Num> Zero <span class="kw">for </span>Complex<T> { |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>zero() -> <span class="self">Self </span>{ |
| <span class="self">Self</span>::new(Zero::zero(), Zero::zero()) |
| } |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>is_zero(<span class="kw-2">&</span><span class="self">self</span>) -> bool { |
| <span class="self">self</span>.re.is_zero() && <span class="self">self</span>.im.is_zero() |
| } |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>set_zero(<span class="kw-2">&mut </span><span class="self">self</span>) { |
| <span class="self">self</span>.re.set_zero(); |
| <span class="self">self</span>.im.set_zero(); |
| } |
| } |
| |
| <span class="kw">impl</span><T: Clone + Num> One <span class="kw">for </span>Complex<T> { |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>one() -> <span class="self">Self </span>{ |
| <span class="self">Self</span>::new(One::one(), Zero::zero()) |
| } |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>is_one(<span class="kw-2">&</span><span class="self">self</span>) -> bool { |
| <span class="self">self</span>.re.is_one() && <span class="self">self</span>.im.is_zero() |
| } |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>set_one(<span class="kw-2">&mut </span><span class="self">self</span>) { |
| <span class="self">self</span>.re.set_one(); |
| <span class="self">self</span>.im.set_zero(); |
| } |
| } |
| |
| <span class="macro">macro_rules! </span>write_complex { |
| (<span class="macro-nonterminal">$f</span>:ident, <span class="macro-nonterminal">$t</span>:expr, <span class="macro-nonterminal">$prefix</span>:expr, <span class="macro-nonterminal">$re</span>:expr, <span class="macro-nonterminal">$im</span>:expr, <span class="macro-nonterminal">$T</span>:ident) => {{ |
| <span class="kw">let </span>abs_re = <span class="kw">if </span><span class="macro-nonterminal">$re </span>< Zero::zero() { |
| <span class="macro-nonterminal">$T::zero</span>() - <span class="macro-nonterminal">$re</span>.clone() |
| } <span class="kw">else </span>{ |
| <span class="macro-nonterminal">$re</span>.clone() |
| }; |
| <span class="kw">let </span>abs_im = <span class="kw">if </span><span class="macro-nonterminal">$im </span>< Zero::zero() { |
| <span class="macro-nonterminal">$T::zero</span>() - <span class="macro-nonterminal">$im</span>.clone() |
| } <span class="kw">else </span>{ |
| <span class="macro-nonterminal">$im</span>.clone() |
| }; |
| |
| <span class="kw">return if let </span><span class="prelude-val">Some</span>(prec) = <span class="macro-nonterminal">$f</span>.precision() { |
| fmt_re_im( |
| <span class="macro-nonterminal">$f</span>, |
| <span class="macro-nonterminal">$re </span>< <span class="macro-nonterminal">$T::zero</span>(), |
| <span class="macro-nonterminal">$im </span>< <span class="macro-nonterminal">$T::zero</span>(), |
| <span class="macro">format_args!</span>(<span class="macro">concat!</span>(<span class="string">"{:.1$"</span>, <span class="macro-nonterminal">$t</span>, <span class="string">"}"</span>), abs_re, prec), |
| <span class="macro">format_args!</span>(<span class="macro">concat!</span>(<span class="string">"{:.1$"</span>, <span class="macro-nonterminal">$t</span>, <span class="string">"}"</span>), abs_im, prec), |
| ) |
| } <span class="kw">else </span>{ |
| fmt_re_im( |
| <span class="macro-nonterminal">$f</span>, |
| <span class="macro-nonterminal">$re </span>< <span class="macro-nonterminal">$T::zero</span>(), |
| <span class="macro-nonterminal">$im </span>< <span class="macro-nonterminal">$T::zero</span>(), |
| <span class="macro">format_args!</span>(<span class="macro">concat!</span>(<span class="string">"{:"</span>, <span class="macro-nonterminal">$t</span>, <span class="string">"}"</span>), abs_re), |
| <span class="macro">format_args!</span>(<span class="macro">concat!</span>(<span class="string">"{:"</span>, <span class="macro-nonterminal">$t</span>, <span class="string">"}"</span>), abs_im), |
| ) |
| }; |
| |
| <span class="kw">fn </span>fmt_re_im( |
| f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>, |
| re_neg: bool, |
| im_neg: bool, |
| real: fmt::Arguments<<span class="lifetime">'_</span>>, |
| imag: fmt::Arguments<<span class="lifetime">'_</span>>, |
| ) -> fmt::Result { |
| <span class="kw">let </span>prefix = <span class="kw">if </span>f.alternate() { <span class="macro-nonterminal">$prefix </span>} <span class="kw">else </span>{ <span class="string">"" </span>}; |
| <span class="kw">let </span>sign = <span class="kw">if </span>re_neg { |
| <span class="string">"-" |
| </span>} <span class="kw">else if </span>f.sign_plus() { |
| <span class="string">"+" |
| </span>} <span class="kw">else </span>{ |
| <span class="string">"" |
| </span>}; |
| |
| <span class="kw">if </span>im_neg { |
| fmt_complex( |
| f, |
| <span class="macro">format_args!</span>( |
| <span class="string">"{}{pre}{re}-{pre}{im}i"</span>, |
| sign, |
| re = real, |
| im = imag, |
| pre = prefix |
| ), |
| ) |
| } <span class="kw">else </span>{ |
| fmt_complex( |
| f, |
| <span class="macro">format_args!</span>( |
| <span class="string">"{}{pre}{re}+{pre}{im}i"</span>, |
| sign, |
| re = real, |
| im = imag, |
| pre = prefix |
| ), |
| ) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| </span><span class="comment">// Currently, we can only apply width using an intermediate `String` (and thus `std`) |
| </span><span class="kw">fn </span>fmt_complex(f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>, complex: fmt::Arguments<<span class="lifetime">'_</span>>) -> fmt::Result { |
| <span class="kw">use </span>std::string::ToString; |
| <span class="kw">if let </span><span class="prelude-val">Some</span>(width) = f.width() { |
| <span class="macro">write!</span>(f, <span class="string">"{0: >1$}"</span>, complex.to_string(), width) |
| } <span class="kw">else </span>{ |
| <span class="macro">write!</span>(f, <span class="string">"{}"</span>, complex) |
| } |
| } |
| |
| <span class="attribute">#[cfg(not(feature = <span class="string">"std"</span>))] |
| </span><span class="kw">fn </span>fmt_complex(f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>, complex: fmt::Arguments<<span class="lifetime">'_</span>>) -> fmt::Result { |
| <span class="macro">write!</span>(f, <span class="string">"{}"</span>, complex) |
| } |
| }}; |
| } |
| |
| <span class="comment">// string conversions |
| </span><span class="kw">impl</span><T> fmt::Display <span class="kw">for </span>Complex<T> |
| <span class="kw">where |
| </span>T: fmt::Display + Num + PartialOrd + Clone, |
| { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| <span class="macro">write_complex!</span>(f, <span class="string">""</span>, <span class="string">""</span>, <span class="self">self</span>.re, <span class="self">self</span>.im, T) |
| } |
| } |
| |
| <span class="kw">impl</span><T> fmt::LowerExp <span class="kw">for </span>Complex<T> |
| <span class="kw">where |
| </span>T: fmt::LowerExp + Num + PartialOrd + Clone, |
| { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| <span class="macro">write_complex!</span>(f, <span class="string">"e"</span>, <span class="string">""</span>, <span class="self">self</span>.re, <span class="self">self</span>.im, T) |
| } |
| } |
| |
| <span class="kw">impl</span><T> fmt::UpperExp <span class="kw">for </span>Complex<T> |
| <span class="kw">where |
| </span>T: fmt::UpperExp + Num + PartialOrd + Clone, |
| { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| <span class="macro">write_complex!</span>(f, <span class="string">"E"</span>, <span class="string">""</span>, <span class="self">self</span>.re, <span class="self">self</span>.im, T) |
| } |
| } |
| |
| <span class="kw">impl</span><T> fmt::LowerHex <span class="kw">for </span>Complex<T> |
| <span class="kw">where |
| </span>T: fmt::LowerHex + Num + PartialOrd + Clone, |
| { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| <span class="macro">write_complex!</span>(f, <span class="string">"x"</span>, <span class="string">"0x"</span>, <span class="self">self</span>.re, <span class="self">self</span>.im, T) |
| } |
| } |
| |
| <span class="kw">impl</span><T> fmt::UpperHex <span class="kw">for </span>Complex<T> |
| <span class="kw">where |
| </span>T: fmt::UpperHex + Num + PartialOrd + Clone, |
| { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| <span class="macro">write_complex!</span>(f, <span class="string">"X"</span>, <span class="string">"0x"</span>, <span class="self">self</span>.re, <span class="self">self</span>.im, T) |
| } |
| } |
| |
| <span class="kw">impl</span><T> fmt::Octal <span class="kw">for </span>Complex<T> |
| <span class="kw">where |
| </span>T: fmt::Octal + Num + PartialOrd + Clone, |
| { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| <span class="macro">write_complex!</span>(f, <span class="string">"o"</span>, <span class="string">"0o"</span>, <span class="self">self</span>.re, <span class="self">self</span>.im, T) |
| } |
| } |
| |
| <span class="kw">impl</span><T> fmt::Binary <span class="kw">for </span>Complex<T> |
| <span class="kw">where |
| </span>T: fmt::Binary + Num + PartialOrd + Clone, |
| { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| <span class="macro">write_complex!</span>(f, <span class="string">"b"</span>, <span class="string">"0b"</span>, <span class="self">self</span>.re, <span class="self">self</span>.im, T) |
| } |
| } |
| |
| <span class="attribute">#[allow(deprecated)] </span><span class="comment">// `trim_left_matches` and `trim_right_matches` since 1.33 |
| </span><span class="kw">fn </span>from_str_generic<T, E, F>(s: <span class="kw-2">&</span>str, from: F) -> <span class="prelude-ty">Result</span><Complex<T>, ParseComplexError<E>> |
| <span class="kw">where |
| </span>F: Fn(<span class="kw-2">&</span>str) -> <span class="prelude-ty">Result</span><T, E>, |
| T: Clone + Num, |
| { |
| <span class="kw">let </span>imag = <span class="kw">match </span>s.rfind(<span class="string">'j'</span>) { |
| <span class="prelude-val">None </span>=> <span class="string">'i'</span>, |
| <span class="kw">_ </span>=> <span class="string">'j'</span>, |
| }; |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>neg_b = <span class="bool-val">false</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>a = s; |
| <span class="kw">let </span><span class="kw-2">mut </span>b = <span class="string">""</span>; |
| |
| <span class="kw">for </span>(i, w) <span class="kw">in </span>s.as_bytes().windows(<span class="number">2</span>).enumerate() { |
| <span class="kw">let </span>p = w[<span class="number">0</span>]; |
| <span class="kw">let </span>c = w[<span class="number">1</span>]; |
| |
| <span class="comment">// ignore '+'/'-' if part of an exponent |
| </span><span class="kw">if </span>(c == <span class="string">b'+' </span>|| c == <span class="string">b'-'</span>) && !(p == <span class="string">b'e' </span>|| p == <span class="string">b'E'</span>) { |
| <span class="comment">// trim whitespace around the separator |
| </span>a = <span class="kw-2">&</span>s[..=i].trim_right_matches(char::is_whitespace); |
| b = <span class="kw-2">&</span>s[i + <span class="number">2</span>..].trim_left_matches(char::is_whitespace); |
| neg_b = c == <span class="string">b'-'</span>; |
| |
| <span class="kw">if </span>b.is_empty() || (neg_b && b.starts_with(<span class="string">'-'</span>)) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(ParseComplexError::new()); |
| } |
| <span class="kw">break</span>; |
| } |
| } |
| |
| <span class="comment">// split off real and imaginary parts |
| </span><span class="kw">if </span>b.is_empty() { |
| <span class="comment">// input was either pure real or pure imaginary |
| </span>b = <span class="kw">if </span>a.ends_with(imag) { <span class="string">"0" </span>} <span class="kw">else </span>{ <span class="string">"0i" </span>}; |
| } |
| |
| <span class="kw">let </span>re; |
| <span class="kw">let </span>neg_re; |
| <span class="kw">let </span>im; |
| <span class="kw">let </span>neg_im; |
| <span class="kw">if </span>a.ends_with(imag) { |
| im = a; |
| neg_im = <span class="bool-val">false</span>; |
| re = b; |
| neg_re = neg_b; |
| } <span class="kw">else if </span>b.ends_with(imag) { |
| re = a; |
| neg_re = <span class="bool-val">false</span>; |
| im = b; |
| neg_im = neg_b; |
| } <span class="kw">else </span>{ |
| <span class="kw">return </span><span class="prelude-val">Err</span>(ParseComplexError::new()); |
| } |
| |
| <span class="comment">// parse re |
| </span><span class="kw">let </span>re = from(re).map_err(ParseComplexError::from_error)<span class="question-mark">?</span>; |
| <span class="kw">let </span>re = <span class="kw">if </span>neg_re { T::zero() - re } <span class="kw">else </span>{ re }; |
| |
| <span class="comment">// pop imaginary unit off |
| </span><span class="kw">let </span><span class="kw-2">mut </span>im = <span class="kw-2">&</span>im[..im.len() - <span class="number">1</span>]; |
| <span class="comment">// handle im == "i" or im == "-i" |
| </span><span class="kw">if </span>im.is_empty() || im == <span class="string">"+" </span>{ |
| im = <span class="string">"1"</span>; |
| } <span class="kw">else if </span>im == <span class="string">"-" </span>{ |
| im = <span class="string">"-1"</span>; |
| } |
| |
| <span class="comment">// parse im |
| </span><span class="kw">let </span>im = from(im).map_err(ParseComplexError::from_error)<span class="question-mark">?</span>; |
| <span class="kw">let </span>im = <span class="kw">if </span>neg_im { T::zero() - im } <span class="kw">else </span>{ im }; |
| |
| <span class="prelude-val">Ok</span>(Complex::new(re, im)) |
| } |
| |
| <span class="kw">impl</span><T> FromStr <span class="kw">for </span>Complex<T> |
| <span class="kw">where |
| </span>T: FromStr + Num + Clone, |
| { |
| <span class="kw">type </span><span class="prelude-val">Err </span>= ParseComplexError<T::Err>; |
| |
| <span class="doccomment">/// Parses `a +/- bi`; `ai +/- b`; `a`; or `bi` where `a` and `b` are of type `T` |
| </span><span class="kw">fn </span>from_str(s: <span class="kw-2">&</span>str) -> <span class="prelude-ty">Result</span><<span class="self">Self</span>, <span class="self">Self</span>::Err> { |
| from_str_generic(s, T::from_str) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Num + Clone> Num <span class="kw">for </span>Complex<T> { |
| <span class="kw">type </span>FromStrRadixErr = ParseComplexError<T::FromStrRadixErr>; |
| |
| <span class="doccomment">/// Parses `a +/- bi`; `ai +/- b`; `a`; or `bi` where `a` and `b` are of type `T` |
| </span><span class="kw">fn </span>from_str_radix(s: <span class="kw-2">&</span>str, radix: u32) -> <span class="prelude-ty">Result</span><<span class="self">Self</span>, <span class="self">Self</span>::FromStrRadixErr> { |
| from_str_generic(s, |x| -> <span class="prelude-ty">Result</span><T, T::FromStrRadixErr> { |
| T::from_str_radix(x, radix) |
| }) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Num + Clone> Sum <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>sum<I>(iter: I) -> <span class="self">Self |
| </span><span class="kw">where |
| </span>I: Iterator<Item = <span class="self">Self</span>>, |
| { |
| iter.fold(<span class="self">Self</span>::zero(), |acc, c| acc + c) |
| } |
| } |
| |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: <span class="lifetime">'a </span>+ Num + Clone> Sum<<span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T>> <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>sum<I>(iter: I) -> <span class="self">Self |
| </span><span class="kw">where |
| </span>I: Iterator<Item = <span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T>>, |
| { |
| iter.fold(<span class="self">Self</span>::zero(), |acc, c| acc + c) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Num + Clone> Product <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>product<I>(iter: I) -> <span class="self">Self |
| </span><span class="kw">where |
| </span>I: Iterator<Item = <span class="self">Self</span>>, |
| { |
| iter.fold(<span class="self">Self</span>::one(), |acc, c| acc * c) |
| } |
| } |
| |
| <span class="kw">impl</span><<span class="lifetime">'a</span>, T: <span class="lifetime">'a </span>+ Num + Clone> Product<<span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T>> <span class="kw">for </span>Complex<T> { |
| <span class="kw">fn </span>product<I>(iter: I) -> <span class="self">Self |
| </span><span class="kw">where |
| </span>I: Iterator<Item = <span class="kw-2">&</span><span class="lifetime">'a </span>Complex<T>>, |
| { |
| iter.fold(<span class="self">Self</span>::one(), |acc, c| acc * c) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"serde"</span>)] |
| </span><span class="kw">impl</span><T> serde::Serialize <span class="kw">for </span>Complex<T> |
| <span class="kw">where |
| </span>T: serde::Serialize, |
| { |
| <span class="kw">fn </span>serialize<S>(<span class="kw-2">&</span><span class="self">self</span>, serializer: S) -> <span class="prelude-ty">Result</span><S::Ok, S::Error> |
| <span class="kw">where |
| </span>S: serde::Serializer, |
| { |
| (<span class="kw-2">&</span><span class="self">self</span>.re, <span class="kw-2">&</span><span class="self">self</span>.im).serialize(serializer) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"serde"</span>)] |
| </span><span class="kw">impl</span><<span class="lifetime">'de</span>, T> serde::Deserialize<<span class="lifetime">'de</span>> <span class="kw">for </span>Complex<T> |
| <span class="kw">where |
| </span>T: serde::Deserialize<<span class="lifetime">'de</span>> + Num + Clone, |
| { |
| <span class="kw">fn </span>deserialize<D>(deserializer: D) -> <span class="prelude-ty">Result</span><<span class="self">Self</span>, D::Error> |
| <span class="kw">where |
| </span>D: serde::Deserializer<<span class="lifetime">'de</span>>, |
| { |
| <span class="kw">let </span>(re, im) = serde::Deserialize::deserialize(deserializer)<span class="question-mark">?</span>; |
| <span class="prelude-val">Ok</span>(<span class="self">Self</span>::new(re, im)) |
| } |
| } |
| |
| <span class="attribute">#[derive(Debug, PartialEq)] |
| </span><span class="kw">pub struct </span>ParseComplexError<E> { |
| kind: ComplexErrorKind<E>, |
| } |
| |
| <span class="attribute">#[derive(Debug, PartialEq)] |
| </span><span class="kw">enum </span>ComplexErrorKind<E> { |
| ParseError(E), |
| ExprError, |
| } |
| |
| <span class="kw">impl</span><E> ParseComplexError<E> { |
| <span class="kw">fn </span>new() -> <span class="self">Self </span>{ |
| ParseComplexError { |
| kind: ComplexErrorKind::ExprError, |
| } |
| } |
| |
| <span class="kw">fn </span>from_error(error: E) -> <span class="self">Self </span>{ |
| ParseComplexError { |
| kind: ComplexErrorKind::ParseError(error), |
| } |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| </span><span class="kw">impl</span><E: Error> Error <span class="kw">for </span>ParseComplexError<E> { |
| <span class="attribute">#[allow(deprecated)] |
| </span><span class="kw">fn </span>description(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>str { |
| <span class="kw">match </span><span class="self">self</span>.kind { |
| ComplexErrorKind::ParseError(<span class="kw-2">ref </span>e) => e.description(), |
| ComplexErrorKind::ExprError => <span class="string">"invalid or unsupported complex expression"</span>, |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><E: fmt::Display> fmt::Display <span class="kw">for </span>ParseComplexError<E> { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| <span class="kw">match </span><span class="self">self</span>.kind { |
| ComplexErrorKind::ParseError(<span class="kw-2">ref </span>e) => e.fmt(f), |
| ComplexErrorKind::ExprError => <span class="string">"invalid or unsupported complex expression"</span>.fmt(f), |
| } |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">fn </span>hash<T: hash::Hash>(x: <span class="kw-2">&</span>T) -> u64 { |
| <span class="kw">use </span>std::collections::hash_map::RandomState; |
| <span class="kw">use </span>std::hash::{BuildHasher, Hasher}; |
| <span class="kw">let </span><span class="kw-2">mut </span>hasher = <RandomState <span class="kw">as </span>BuildHasher>::Hasher::new(); |
| x.hash(<span class="kw-2">&mut </span>hasher); |
| hasher.finish() |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>test { |
| <span class="attribute">#![allow(non_upper_case_globals)] |
| |
| </span><span class="kw">use super</span>::{Complex, Complex64}; |
| <span class="kw">use </span>core::f64; |
| <span class="kw">use </span>core::str::FromStr; |
| |
| <span class="kw">use </span>std::string::{String, ToString}; |
| |
| <span class="kw">use </span>num_traits::{Num, One, Zero}; |
| |
| <span class="kw">pub const </span>_0_0i: Complex64 = Complex { re: <span class="number">0.0</span>, im: <span class="number">0.0 </span>}; |
| <span class="kw">pub const </span>_1_0i: Complex64 = Complex { re: <span class="number">1.0</span>, im: <span class="number">0.0 </span>}; |
| <span class="kw">pub const </span>_1_1i: Complex64 = Complex { re: <span class="number">1.0</span>, im: <span class="number">1.0 </span>}; |
| <span class="kw">pub const </span>_0_1i: Complex64 = Complex { re: <span class="number">0.0</span>, im: <span class="number">1.0 </span>}; |
| <span class="kw">pub const </span>_neg1_1i: Complex64 = Complex { re: -<span class="number">1.0</span>, im: <span class="number">1.0 </span>}; |
| <span class="kw">pub const </span>_05_05i: Complex64 = Complex { re: <span class="number">0.5</span>, im: <span class="number">0.5 </span>}; |
| <span class="kw">pub const </span>all_consts: [Complex64; <span class="number">5</span>] = [_0_0i, _1_0i, _1_1i, _neg1_1i, _05_05i]; |
| <span class="kw">pub const </span>_4_2i: Complex64 = Complex { re: <span class="number">4.0</span>, im: <span class="number">2.0 </span>}; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_consts() { |
| <span class="comment">// check our constants are what Complex::new creates |
| </span><span class="kw">fn </span>test(c: Complex64, r: f64, i: f64) { |
| <span class="macro">assert_eq!</span>(c, Complex::new(r, i)); |
| } |
| test(_0_0i, <span class="number">0.0</span>, <span class="number">0.0</span>); |
| test(_1_0i, <span class="number">1.0</span>, <span class="number">0.0</span>); |
| test(_1_1i, <span class="number">1.0</span>, <span class="number">1.0</span>); |
| test(_neg1_1i, -<span class="number">1.0</span>, <span class="number">1.0</span>); |
| test(_05_05i, <span class="number">0.5</span>, <span class="number">0.5</span>); |
| |
| <span class="macro">assert_eq!</span>(_0_0i, Zero::zero()); |
| <span class="macro">assert_eq!</span>(_1_0i, One::one()); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_scale_unscale() { |
| <span class="macro">assert_eq!</span>(_05_05i.scale(<span class="number">2.0</span>), _1_1i); |
| <span class="macro">assert_eq!</span>(_1_1i.unscale(<span class="number">2.0</span>), _05_05i); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="macro">assert_eq!</span>(c.scale(<span class="number">2.0</span>).unscale(<span class="number">2.0</span>), c); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_conj() { |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="macro">assert_eq!</span>(c.conj(), Complex::new(c.re, -c.im)); |
| <span class="macro">assert_eq!</span>(c.conj().conj(), c); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_inv() { |
| <span class="macro">assert_eq!</span>(_1_1i.inv(), _05_05i.conj()); |
| <span class="macro">assert_eq!</span>(_1_0i.inv(), _1_0i.inv()); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_divide_by_zero_natural() { |
| <span class="kw">let </span>n = Complex::new(<span class="number">2</span>, <span class="number">3</span>); |
| <span class="kw">let </span>d = Complex::new(<span class="number">0</span>, <span class="number">0</span>); |
| <span class="kw">let </span>_x = n / d; |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_inv_zero() { |
| <span class="comment">// FIXME #20: should this really fail, or just NaN? |
| </span><span class="macro">assert!</span>(_0_0i.inv().is_nan()); |
| } |
| |
| <span class="attribute">#[test] |
| #[allow(clippy::float_cmp)] |
| </span><span class="kw">fn </span>test_l1_norm() { |
| <span class="macro">assert_eq!</span>(_0_0i.l1_norm(), <span class="number">0.0</span>); |
| <span class="macro">assert_eq!</span>(_1_0i.l1_norm(), <span class="number">1.0</span>); |
| <span class="macro">assert_eq!</span>(_1_1i.l1_norm(), <span class="number">2.0</span>); |
| <span class="macro">assert_eq!</span>(_0_1i.l1_norm(), <span class="number">1.0</span>); |
| <span class="macro">assert_eq!</span>(_neg1_1i.l1_norm(), <span class="number">2.0</span>); |
| <span class="macro">assert_eq!</span>(_05_05i.l1_norm(), <span class="number">1.0</span>); |
| <span class="macro">assert_eq!</span>(_4_2i.l1_norm(), <span class="number">6.0</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_pow() { |
| <span class="kw">for </span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="macro">assert_eq!</span>(c.powi(<span class="number">0</span>), _1_0i); |
| <span class="kw">let </span><span class="kw-2">mut </span>pos = _1_0i; |
| <span class="kw">let </span><span class="kw-2">mut </span>neg = _1_0i; |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">1i32</span>..<span class="number">20 </span>{ |
| pos <span class="kw-2">*</span>= c; |
| <span class="macro">assert_eq!</span>(pos, c.powi(i)); |
| <span class="kw">if </span>c.is_zero() { |
| <span class="macro">assert!</span>(c.powi(-i).is_nan()); |
| } <span class="kw">else </span>{ |
| neg /= c; |
| <span class="macro">assert_eq!</span>(neg, c.powi(-i)); |
| } |
| } |
| } |
| } |
| |
| <span class="attribute">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))] |
| </span><span class="kw">mod </span>float { |
| <span class="kw">use super</span>::<span class="kw-2">*</span>; |
| <span class="kw">use </span>num_traits::{Float, Pow}; |
| |
| <span class="attribute">#[test] |
| #[cfg_attr(target_arch = <span class="string">"x86"</span>, ignore)] |
| </span><span class="comment">// FIXME #7158: (maybe?) currently failing on x86. |
| </span><span class="attribute">#[allow(clippy::float_cmp)] |
| </span><span class="kw">fn </span>test_norm() { |
| <span class="kw">fn </span>test(c: Complex64, ns: f64) { |
| <span class="macro">assert_eq!</span>(c.norm_sqr(), ns); |
| <span class="macro">assert_eq!</span>(c.norm(), ns.sqrt()) |
| } |
| test(_0_0i, <span class="number">0.0</span>); |
| test(_1_0i, <span class="number">1.0</span>); |
| test(_1_1i, <span class="number">2.0</span>); |
| test(_neg1_1i, <span class="number">2.0</span>); |
| test(_05_05i, <span class="number">0.5</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_arg() { |
| <span class="kw">fn </span>test(c: Complex64, arg: f64) { |
| <span class="macro">assert!</span>((c.arg() - arg).abs() < <span class="number">1.0e-6</span>) |
| } |
| test(_1_0i, <span class="number">0.0</span>); |
| test(_1_1i, <span class="number">0.25 </span>* f64::consts::PI); |
| test(_neg1_1i, <span class="number">0.75 </span>* f64::consts::PI); |
| test(_05_05i, <span class="number">0.25 </span>* f64::consts::PI); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_polar_conv() { |
| <span class="kw">fn </span>test(c: Complex64) { |
| <span class="kw">let </span>(r, theta) = c.to_polar(); |
| <span class="macro">assert!</span>((c - Complex::from_polar(r, theta)).norm() < <span class="number">1e-6</span>); |
| } |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| test(c); |
| } |
| } |
| |
| <span class="kw">fn </span>close(a: Complex64, b: Complex64) -> bool { |
| close_to_tol(a, b, <span class="number">1e-10</span>) |
| } |
| |
| <span class="kw">fn </span>close_to_tol(a: Complex64, b: Complex64, tol: f64) -> bool { |
| <span class="comment">// returns true if a and b are reasonably close |
| </span><span class="kw">let </span>close = (a == b) || (a - b).norm() < tol; |
| <span class="kw">if </span>!close { |
| <span class="macro">println!</span>(<span class="string">"{:?} != {:?}"</span>, a, b); |
| } |
| close |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_exp() { |
| <span class="macro">assert!</span>(close(_1_0i.exp(), _1_0i.scale(f64::consts::E))); |
| <span class="macro">assert!</span>(close(_0_0i.exp(), _1_0i)); |
| <span class="macro">assert!</span>(close(_0_1i.exp(), Complex::new(<span class="number">1.0</span>.cos(), <span class="number">1.0</span>.sin()))); |
| <span class="macro">assert!</span>(close(_05_05i.exp() * _05_05i.exp(), _1_1i.exp())); |
| <span class="macro">assert!</span>(close( |
| _0_1i.scale(-f64::consts::PI).exp(), |
| _1_0i.scale(-<span class="number">1.0</span>) |
| )); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// e^conj(z) = conj(e^z) |
| </span><span class="macro">assert!</span>(close(c.conj().exp(), c.exp().conj())); |
| <span class="comment">// e^(z + 2 pi i) = e^z |
| </span><span class="macro">assert!</span>(close( |
| c.exp(), |
| (c + _0_1i.scale(f64::consts::PI * <span class="number">2.0</span>)).exp() |
| )); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_ln() { |
| <span class="macro">assert!</span>(close(_1_0i.ln(), _0_0i)); |
| <span class="macro">assert!</span>(close(_0_1i.ln(), _0_1i.scale(f64::consts::PI / <span class="number">2.0</span>))); |
| <span class="macro">assert!</span>(close(_0_0i.ln(), Complex::new(f64::neg_infinity(), <span class="number">0.0</span>))); |
| <span class="macro">assert!</span>(close( |
| (_neg1_1i * _05_05i).ln(), |
| _neg1_1i.ln() + _05_05i.ln() |
| )); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// ln(conj(z() = conj(ln(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().ln(), c.ln().conj())); |
| <span class="comment">// for this branch, -pi <= arg(ln(z)) <= pi |
| </span><span class="macro">assert!</span>(-f64::consts::PI <= c.ln().arg() && c.ln().arg() <= f64::consts::PI); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_powc() { |
| <span class="kw">let </span>a = Complex::new(<span class="number">2.0</span>, -<span class="number">3.0</span>); |
| <span class="kw">let </span>b = Complex::new(<span class="number">3.0</span>, <span class="number">0.0</span>); |
| <span class="macro">assert!</span>(close(a.powc(b), a.powf(b.re))); |
| <span class="macro">assert!</span>(close(b.powc(a), a.expf(b.re))); |
| <span class="kw">let </span>c = Complex::new(<span class="number">1.0 </span>/ <span class="number">3.0</span>, <span class="number">0.1</span>); |
| <span class="macro">assert!</span>(close_to_tol( |
| a.powc(c), |
| Complex::new(<span class="number">1.65826</span>, -<span class="number">0.33502</span>), |
| <span class="number">1e-5 |
| </span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_powf() { |
| <span class="kw">let </span>c = Complex64::new(<span class="number">2.0</span>, -<span class="number">1.0</span>); |
| <span class="kw">let </span>expected = Complex64::new(-<span class="number">0.8684746</span>, -<span class="number">16.695934</span>); |
| <span class="macro">assert!</span>(close_to_tol(c.powf(<span class="number">3.5</span>), expected, <span class="number">1e-5</span>)); |
| <span class="macro">assert!</span>(close_to_tol(Pow::pow(c, <span class="number">3.5_f64</span>), expected, <span class="number">1e-5</span>)); |
| <span class="macro">assert!</span>(close_to_tol(Pow::pow(c, <span class="number">3.5_f32</span>), expected, <span class="number">1e-5</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_log() { |
| <span class="kw">let </span>c = Complex::new(<span class="number">2.0</span>, -<span class="number">1.0</span>); |
| <span class="kw">let </span>r = c.log(<span class="number">10.0</span>); |
| <span class="macro">assert!</span>(close_to_tol(r, Complex::new(<span class="number">0.349485</span>, -<span class="number">0.20135958</span>), <span class="number">1e-5</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_some_expf_cases() { |
| <span class="kw">let </span>c = Complex::new(<span class="number">2.0</span>, -<span class="number">1.0</span>); |
| <span class="kw">let </span>r = c.expf(<span class="number">10.0</span>); |
| <span class="macro">assert!</span>(close_to_tol(r, Complex::new(-<span class="number">66.82015</span>, -<span class="number">74.39803</span>), <span class="number">1e-5</span>)); |
| |
| <span class="kw">let </span>c = Complex::new(<span class="number">5.0</span>, -<span class="number">2.0</span>); |
| <span class="kw">let </span>r = c.expf(<span class="number">3.4</span>); |
| <span class="macro">assert!</span>(close_to_tol(r, Complex::new(-<span class="number">349.25</span>, -<span class="number">290.63</span>), <span class="number">1e-2</span>)); |
| |
| <span class="kw">let </span>c = Complex::new(-<span class="number">1.5</span>, <span class="number">2.0 </span>/ <span class="number">3.0</span>); |
| <span class="kw">let </span>r = c.expf(<span class="number">1.0 </span>/ <span class="number">3.0</span>); |
| <span class="macro">assert!</span>(close_to_tol(r, Complex::new(<span class="number">3.8637</span>, -<span class="number">3.4745</span>), <span class="number">1e-2</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_sqrt() { |
| <span class="macro">assert!</span>(close(_0_0i.sqrt(), _0_0i)); |
| <span class="macro">assert!</span>(close(_1_0i.sqrt(), _1_0i)); |
| <span class="macro">assert!</span>(close(Complex::new(-<span class="number">1.0</span>, <span class="number">0.0</span>).sqrt(), _0_1i)); |
| <span class="macro">assert!</span>(close(Complex::new(-<span class="number">1.0</span>, -<span class="number">0.0</span>).sqrt(), _0_1i.scale(-<span class="number">1.0</span>))); |
| <span class="macro">assert!</span>(close(_0_1i.sqrt(), _05_05i.scale(<span class="number">2.0</span>.sqrt()))); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// sqrt(conj(z() = conj(sqrt(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().sqrt(), c.sqrt().conj())); |
| <span class="comment">// for this branch, -pi/2 <= arg(sqrt(z)) <= pi/2 |
| </span><span class="macro">assert!</span>( |
| -f64::consts::FRAC_PI_2 <= c.sqrt().arg() |
| && c.sqrt().arg() <= f64::consts::FRAC_PI_2 |
| ); |
| <span class="comment">// sqrt(z) * sqrt(z) = z |
| </span><span class="macro">assert!</span>(close(c.sqrt() * c.sqrt(), c)); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_sqrt_real() { |
| <span class="kw">for </span>n <span class="kw">in </span>(<span class="number">0</span>..<span class="number">100</span>).map(f64::from) { |
| <span class="comment">// √(n² + 0i) = n + 0i |
| </span><span class="kw">let </span>n2 = n * n; |
| <span class="macro">assert_eq!</span>(Complex64::new(n2, <span class="number">0.0</span>).sqrt(), Complex64::new(n, <span class="number">0.0</span>)); |
| <span class="comment">// √(-n² + 0i) = 0 + ni |
| </span><span class="macro">assert_eq!</span>(Complex64::new(-n2, <span class="number">0.0</span>).sqrt(), Complex64::new(<span class="number">0.0</span>, n)); |
| <span class="comment">// √(-n² - 0i) = 0 - ni |
| </span><span class="macro">assert_eq!</span>(Complex64::new(-n2, -<span class="number">0.0</span>).sqrt(), Complex64::new(<span class="number">0.0</span>, -n)); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_sqrt_imag() { |
| <span class="kw">for </span>n <span class="kw">in </span>(<span class="number">0</span>..<span class="number">100</span>).map(f64::from) { |
| <span class="comment">// √(0 + n²i) = n e^(iπ/4) |
| </span><span class="kw">let </span>n2 = n * n; |
| <span class="macro">assert!</span>(close( |
| Complex64::new(<span class="number">0.0</span>, n2).sqrt(), |
| Complex64::from_polar(n, f64::consts::FRAC_PI_4) |
| )); |
| <span class="comment">// √(0 - n²i) = n e^(-iπ/4) |
| </span><span class="macro">assert!</span>(close( |
| Complex64::new(<span class="number">0.0</span>, -n2).sqrt(), |
| Complex64::from_polar(n, -f64::consts::FRAC_PI_4) |
| )); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_cbrt() { |
| <span class="macro">assert!</span>(close(_0_0i.cbrt(), _0_0i)); |
| <span class="macro">assert!</span>(close(_1_0i.cbrt(), _1_0i)); |
| <span class="macro">assert!</span>(close( |
| Complex::new(-<span class="number">1.0</span>, <span class="number">0.0</span>).cbrt(), |
| Complex::new(<span class="number">0.5</span>, <span class="number">0.75</span>.sqrt()) |
| )); |
| <span class="macro">assert!</span>(close( |
| Complex::new(-<span class="number">1.0</span>, -<span class="number">0.0</span>).cbrt(), |
| Complex::new(<span class="number">0.5</span>, -(<span class="number">0.75</span>.sqrt())) |
| )); |
| <span class="macro">assert!</span>(close(_0_1i.cbrt(), Complex::new(<span class="number">0.75</span>.sqrt(), <span class="number">0.5</span>))); |
| <span class="macro">assert!</span>(close(_0_1i.conj().cbrt(), Complex::new(<span class="number">0.75</span>.sqrt(), -<span class="number">0.5</span>))); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// cbrt(conj(z() = conj(cbrt(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().cbrt(), c.cbrt().conj())); |
| <span class="comment">// for this branch, -pi/3 <= arg(cbrt(z)) <= pi/3 |
| </span><span class="macro">assert!</span>( |
| -f64::consts::FRAC_PI_3 <= c.cbrt().arg() |
| && c.cbrt().arg() <= f64::consts::FRAC_PI_3 |
| ); |
| <span class="comment">// cbrt(z) * cbrt(z) cbrt(z) = z |
| </span><span class="macro">assert!</span>(close(c.cbrt() * c.cbrt() * c.cbrt(), c)); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_cbrt_real() { |
| <span class="kw">for </span>n <span class="kw">in </span>(<span class="number">0</span>..<span class="number">100</span>).map(f64::from) { |
| <span class="comment">// ∛(n³ + 0i) = n + 0i |
| </span><span class="kw">let </span>n3 = n * n * n; |
| <span class="macro">assert!</span>(close( |
| Complex64::new(n3, <span class="number">0.0</span>).cbrt(), |
| Complex64::new(n, <span class="number">0.0</span>) |
| )); |
| <span class="comment">// ∛(-n³ + 0i) = n e^(iπ/3) |
| </span><span class="macro">assert!</span>(close( |
| Complex64::new(-n3, <span class="number">0.0</span>).cbrt(), |
| Complex64::from_polar(n, f64::consts::FRAC_PI_3) |
| )); |
| <span class="comment">// ∛(-n³ - 0i) = n e^(-iπ/3) |
| </span><span class="macro">assert!</span>(close( |
| Complex64::new(-n3, -<span class="number">0.0</span>).cbrt(), |
| Complex64::from_polar(n, -f64::consts::FRAC_PI_3) |
| )); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_cbrt_imag() { |
| <span class="kw">for </span>n <span class="kw">in </span>(<span class="number">0</span>..<span class="number">100</span>).map(f64::from) { |
| <span class="comment">// ∛(0 + n³i) = n e^(iπ/6) |
| </span><span class="kw">let </span>n3 = n * n * n; |
| <span class="macro">assert!</span>(close( |
| Complex64::new(<span class="number">0.0</span>, n3).cbrt(), |
| Complex64::from_polar(n, f64::consts::FRAC_PI_6) |
| )); |
| <span class="comment">// ∛(0 - n³i) = n e^(-iπ/6) |
| </span><span class="macro">assert!</span>(close( |
| Complex64::new(<span class="number">0.0</span>, -n3).cbrt(), |
| Complex64::from_polar(n, -f64::consts::FRAC_PI_6) |
| )); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_sin() { |
| <span class="macro">assert!</span>(close(_0_0i.sin(), _0_0i)); |
| <span class="macro">assert!</span>(close(_1_0i.scale(f64::consts::PI * <span class="number">2.0</span>).sin(), _0_0i)); |
| <span class="macro">assert!</span>(close(_0_1i.sin(), _0_1i.scale(<span class="number">1.0</span>.sinh()))); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// sin(conj(z)) = conj(sin(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().sin(), c.sin().conj())); |
| <span class="comment">// sin(-z) = -sin(z) |
| </span><span class="macro">assert!</span>(close(c.scale(-<span class="number">1.0</span>).sin(), c.sin().scale(-<span class="number">1.0</span>))); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_cos() { |
| <span class="macro">assert!</span>(close(_0_0i.cos(), _1_0i)); |
| <span class="macro">assert!</span>(close(_1_0i.scale(f64::consts::PI * <span class="number">2.0</span>).cos(), _1_0i)); |
| <span class="macro">assert!</span>(close(_0_1i.cos(), _1_0i.scale(<span class="number">1.0</span>.cosh()))); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// cos(conj(z)) = conj(cos(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().cos(), c.cos().conj())); |
| <span class="comment">// cos(-z) = cos(z) |
| </span><span class="macro">assert!</span>(close(c.scale(-<span class="number">1.0</span>).cos(), c.cos())); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_tan() { |
| <span class="macro">assert!</span>(close(_0_0i.tan(), _0_0i)); |
| <span class="macro">assert!</span>(close(_1_0i.scale(f64::consts::PI / <span class="number">4.0</span>).tan(), _1_0i)); |
| <span class="macro">assert!</span>(close(_1_0i.scale(f64::consts::PI).tan(), _0_0i)); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// tan(conj(z)) = conj(tan(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().tan(), c.tan().conj())); |
| <span class="comment">// tan(-z) = -tan(z) |
| </span><span class="macro">assert!</span>(close(c.scale(-<span class="number">1.0</span>).tan(), c.tan().scale(-<span class="number">1.0</span>))); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_asin() { |
| <span class="macro">assert!</span>(close(_0_0i.asin(), _0_0i)); |
| <span class="macro">assert!</span>(close(_1_0i.asin(), _1_0i.scale(f64::consts::PI / <span class="number">2.0</span>))); |
| <span class="macro">assert!</span>(close( |
| _1_0i.scale(-<span class="number">1.0</span>).asin(), |
| _1_0i.scale(-f64::consts::PI / <span class="number">2.0</span>) |
| )); |
| <span class="macro">assert!</span>(close(_0_1i.asin(), _0_1i.scale((<span class="number">1.0 </span>+ <span class="number">2.0</span>.sqrt()).ln()))); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// asin(conj(z)) = conj(asin(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().asin(), c.asin().conj())); |
| <span class="comment">// asin(-z) = -asin(z) |
| </span><span class="macro">assert!</span>(close(c.scale(-<span class="number">1.0</span>).asin(), c.asin().scale(-<span class="number">1.0</span>))); |
| <span class="comment">// for this branch, -pi/2 <= asin(z).re <= pi/2 |
| </span><span class="macro">assert!</span>( |
| -f64::consts::PI / <span class="number">2.0 </span><= c.asin().re && c.asin().re <= f64::consts::PI / <span class="number">2.0 |
| </span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_acos() { |
| <span class="macro">assert!</span>(close(_0_0i.acos(), _1_0i.scale(f64::consts::PI / <span class="number">2.0</span>))); |
| <span class="macro">assert!</span>(close(_1_0i.acos(), _0_0i)); |
| <span class="macro">assert!</span>(close( |
| _1_0i.scale(-<span class="number">1.0</span>).acos(), |
| _1_0i.scale(f64::consts::PI) |
| )); |
| <span class="macro">assert!</span>(close( |
| _0_1i.acos(), |
| Complex::new(f64::consts::PI / <span class="number">2.0</span>, (<span class="number">2.0</span>.sqrt() - <span class="number">1.0</span>).ln()) |
| )); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// acos(conj(z)) = conj(acos(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().acos(), c.acos().conj())); |
| <span class="comment">// for this branch, 0 <= acos(z).re <= pi |
| </span><span class="macro">assert!</span>(<span class="number">0.0 </span><= c.acos().re && c.acos().re <= f64::consts::PI); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_atan() { |
| <span class="macro">assert!</span>(close(_0_0i.atan(), _0_0i)); |
| <span class="macro">assert!</span>(close(_1_0i.atan(), _1_0i.scale(f64::consts::PI / <span class="number">4.0</span>))); |
| <span class="macro">assert!</span>(close( |
| _1_0i.scale(-<span class="number">1.0</span>).atan(), |
| _1_0i.scale(-f64::consts::PI / <span class="number">4.0</span>) |
| )); |
| <span class="macro">assert!</span>(close(_0_1i.atan(), Complex::new(<span class="number">0.0</span>, f64::infinity()))); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// atan(conj(z)) = conj(atan(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().atan(), c.atan().conj())); |
| <span class="comment">// atan(-z) = -atan(z) |
| </span><span class="macro">assert!</span>(close(c.scale(-<span class="number">1.0</span>).atan(), c.atan().scale(-<span class="number">1.0</span>))); |
| <span class="comment">// for this branch, -pi/2 <= atan(z).re <= pi/2 |
| </span><span class="macro">assert!</span>( |
| -f64::consts::PI / <span class="number">2.0 </span><= c.atan().re && c.atan().re <= f64::consts::PI / <span class="number">2.0 |
| </span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_sinh() { |
| <span class="macro">assert!</span>(close(_0_0i.sinh(), _0_0i)); |
| <span class="macro">assert!</span>(close( |
| _1_0i.sinh(), |
| _1_0i.scale((f64::consts::E - <span class="number">1.0 </span>/ f64::consts::E) / <span class="number">2.0</span>) |
| )); |
| <span class="macro">assert!</span>(close(_0_1i.sinh(), _0_1i.scale(<span class="number">1.0</span>.sin()))); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// sinh(conj(z)) = conj(sinh(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().sinh(), c.sinh().conj())); |
| <span class="comment">// sinh(-z) = -sinh(z) |
| </span><span class="macro">assert!</span>(close(c.scale(-<span class="number">1.0</span>).sinh(), c.sinh().scale(-<span class="number">1.0</span>))); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_cosh() { |
| <span class="macro">assert!</span>(close(_0_0i.cosh(), _1_0i)); |
| <span class="macro">assert!</span>(close( |
| _1_0i.cosh(), |
| _1_0i.scale((f64::consts::E + <span class="number">1.0 </span>/ f64::consts::E) / <span class="number">2.0</span>) |
| )); |
| <span class="macro">assert!</span>(close(_0_1i.cosh(), _1_0i.scale(<span class="number">1.0</span>.cos()))); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// cosh(conj(z)) = conj(cosh(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().cosh(), c.cosh().conj())); |
| <span class="comment">// cosh(-z) = cosh(z) |
| </span><span class="macro">assert!</span>(close(c.scale(-<span class="number">1.0</span>).cosh(), c.cosh())); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_tanh() { |
| <span class="macro">assert!</span>(close(_0_0i.tanh(), _0_0i)); |
| <span class="macro">assert!</span>(close( |
| _1_0i.tanh(), |
| _1_0i.scale((f64::consts::E.powi(<span class="number">2</span>) - <span class="number">1.0</span>) / (f64::consts::E.powi(<span class="number">2</span>) + <span class="number">1.0</span>)) |
| )); |
| <span class="macro">assert!</span>(close(_0_1i.tanh(), _0_1i.scale(<span class="number">1.0</span>.tan()))); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// tanh(conj(z)) = conj(tanh(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().tanh(), c.conj().tanh())); |
| <span class="comment">// tanh(-z) = -tanh(z) |
| </span><span class="macro">assert!</span>(close(c.scale(-<span class="number">1.0</span>).tanh(), c.tanh().scale(-<span class="number">1.0</span>))); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_asinh() { |
| <span class="macro">assert!</span>(close(_0_0i.asinh(), _0_0i)); |
| <span class="macro">assert!</span>(close(_1_0i.asinh(), _1_0i.scale(<span class="number">1.0 </span>+ <span class="number">2.0</span>.sqrt()).ln())); |
| <span class="macro">assert!</span>(close(_0_1i.asinh(), _0_1i.scale(f64::consts::PI / <span class="number">2.0</span>))); |
| <span class="macro">assert!</span>(close( |
| _0_1i.asinh().scale(-<span class="number">1.0</span>), |
| _0_1i.scale(-f64::consts::PI / <span class="number">2.0</span>) |
| )); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// asinh(conj(z)) = conj(asinh(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().asinh(), c.conj().asinh())); |
| <span class="comment">// asinh(-z) = -asinh(z) |
| </span><span class="macro">assert!</span>(close(c.scale(-<span class="number">1.0</span>).asinh(), c.asinh().scale(-<span class="number">1.0</span>))); |
| <span class="comment">// for this branch, -pi/2 <= asinh(z).im <= pi/2 |
| </span><span class="macro">assert!</span>( |
| -f64::consts::PI / <span class="number">2.0 </span><= c.asinh().im && c.asinh().im <= f64::consts::PI / <span class="number">2.0 |
| </span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_acosh() { |
| <span class="macro">assert!</span>(close(_0_0i.acosh(), _0_1i.scale(f64::consts::PI / <span class="number">2.0</span>))); |
| <span class="macro">assert!</span>(close(_1_0i.acosh(), _0_0i)); |
| <span class="macro">assert!</span>(close( |
| _1_0i.scale(-<span class="number">1.0</span>).acosh(), |
| _0_1i.scale(f64::consts::PI) |
| )); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// acosh(conj(z)) = conj(acosh(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().acosh(), c.conj().acosh())); |
| <span class="comment">// for this branch, -pi <= acosh(z).im <= pi and 0 <= acosh(z).re |
| </span><span class="macro">assert!</span>( |
| -f64::consts::PI <= c.acosh().im |
| && c.acosh().im <= f64::consts::PI |
| && <span class="number">0.0 </span><= c.cosh().re |
| ); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_atanh() { |
| <span class="macro">assert!</span>(close(_0_0i.atanh(), _0_0i)); |
| <span class="macro">assert!</span>(close(_0_1i.atanh(), _0_1i.scale(f64::consts::PI / <span class="number">4.0</span>))); |
| <span class="macro">assert!</span>(close(_1_0i.atanh(), Complex::new(f64::infinity(), <span class="number">0.0</span>))); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// atanh(conj(z)) = conj(atanh(z)) |
| </span><span class="macro">assert!</span>(close(c.conj().atanh(), c.conj().atanh())); |
| <span class="comment">// atanh(-z) = -atanh(z) |
| </span><span class="macro">assert!</span>(close(c.scale(-<span class="number">1.0</span>).atanh(), c.atanh().scale(-<span class="number">1.0</span>))); |
| <span class="comment">// for this branch, -pi/2 <= atanh(z).im <= pi/2 |
| </span><span class="macro">assert!</span>( |
| -f64::consts::PI / <span class="number">2.0 </span><= c.atanh().im && c.atanh().im <= f64::consts::PI / <span class="number">2.0 |
| </span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_exp_ln() { |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// e^ln(z) = z |
| </span><span class="macro">assert!</span>(close(c.ln().exp(), c)); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_trig_to_hyperbolic() { |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// sin(iz) = i sinh(z) |
| </span><span class="macro">assert!</span>(close((_0_1i * c).sin(), _0_1i * c.sinh())); |
| <span class="comment">// cos(iz) = cosh(z) |
| </span><span class="macro">assert!</span>(close((_0_1i * c).cos(), c.cosh())); |
| <span class="comment">// tan(iz) = i tanh(z) |
| </span><span class="macro">assert!</span>(close((_0_1i * c).tan(), _0_1i * c.tanh())); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_trig_identities() { |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// tan(z) = sin(z)/cos(z) |
| </span><span class="macro">assert!</span>(close(c.tan(), c.sin() / c.cos())); |
| <span class="comment">// sin(z)^2 + cos(z)^2 = 1 |
| </span><span class="macro">assert!</span>(close(c.sin() * c.sin() + c.cos() * c.cos(), _1_0i)); |
| |
| <span class="comment">// sin(asin(z)) = z |
| </span><span class="macro">assert!</span>(close(c.asin().sin(), c)); |
| <span class="comment">// cos(acos(z)) = z |
| </span><span class="macro">assert!</span>(close(c.acos().cos(), c)); |
| <span class="comment">// tan(atan(z)) = z |
| // i and -i are branch points |
| </span><span class="kw">if </span>c != _0_1i && c != _0_1i.scale(-<span class="number">1.0</span>) { |
| <span class="macro">assert!</span>(close(c.atan().tan(), c)); |
| } |
| |
| <span class="comment">// sin(z) = (e^(iz) - e^(-iz))/(2i) |
| </span><span class="macro">assert!</span>(close( |
| ((_0_1i * c).exp() - (_0_1i * c).exp().inv()) / _0_1i.scale(<span class="number">2.0</span>), |
| c.sin() |
| )); |
| <span class="comment">// cos(z) = (e^(iz) + e^(-iz))/2 |
| </span><span class="macro">assert!</span>(close( |
| ((_0_1i * c).exp() + (_0_1i * c).exp().inv()).unscale(<span class="number">2.0</span>), |
| c.cos() |
| )); |
| <span class="comment">// tan(z) = i (1 - e^(2iz))/(1 + e^(2iz)) |
| </span><span class="macro">assert!</span>(close( |
| _0_1i * (_1_0i - (_0_1i * c).scale(<span class="number">2.0</span>).exp()) |
| / (_1_0i + (_0_1i * c).scale(<span class="number">2.0</span>).exp()), |
| c.tan() |
| )); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_hyperbolic_identites() { |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="comment">// tanh(z) = sinh(z)/cosh(z) |
| </span><span class="macro">assert!</span>(close(c.tanh(), c.sinh() / c.cosh())); |
| <span class="comment">// cosh(z)^2 - sinh(z)^2 = 1 |
| </span><span class="macro">assert!</span>(close(c.cosh() * c.cosh() - c.sinh() * c.sinh(), _1_0i)); |
| |
| <span class="comment">// sinh(asinh(z)) = z |
| </span><span class="macro">assert!</span>(close(c.asinh().sinh(), c)); |
| <span class="comment">// cosh(acosh(z)) = z |
| </span><span class="macro">assert!</span>(close(c.acosh().cosh(), c)); |
| <span class="comment">// tanh(atanh(z)) = z |
| // 1 and -1 are branch points |
| </span><span class="kw">if </span>c != _1_0i && c != _1_0i.scale(-<span class="number">1.0</span>) { |
| <span class="macro">assert!</span>(close(c.atanh().tanh(), c)); |
| } |
| |
| <span class="comment">// sinh(z) = (e^z - e^(-z))/2 |
| </span><span class="macro">assert!</span>(close((c.exp() - c.exp().inv()).unscale(<span class="number">2.0</span>), c.sinh())); |
| <span class="comment">// cosh(z) = (e^z + e^(-z))/2 |
| </span><span class="macro">assert!</span>(close((c.exp() + c.exp().inv()).unscale(<span class="number">2.0</span>), c.cosh())); |
| <span class="comment">// tanh(z) = ( e^(2z) - 1)/(e^(2z) + 1) |
| </span><span class="macro">assert!</span>(close( |
| (c.scale(<span class="number">2.0</span>).exp() - _1_0i) / (c.scale(<span class="number">2.0</span>).exp() + _1_0i), |
| c.tanh() |
| )); |
| } |
| } |
| } |
| |
| <span class="comment">// Test both a + b and a += b |
| </span><span class="macro">macro_rules! </span>test_a_op_b { |
| (<span class="macro-nonterminal">$a</span>:ident + <span class="macro-nonterminal">$b</span>:expr, <span class="macro-nonterminal">$answer</span>:expr) => { |
| <span class="macro">assert_eq!</span>(<span class="macro-nonterminal">$a </span>+ <span class="macro-nonterminal">$b</span>, <span class="macro-nonterminal">$answer</span>); |
| <span class="macro">assert_eq!</span>( |
| { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro-nonterminal">$a</span>; |
| x += <span class="macro-nonterminal">$b</span>; |
| x |
| }, |
| <span class="macro-nonterminal">$answer |
| </span>); |
| }; |
| (<span class="macro-nonterminal">$a</span>:ident - <span class="macro-nonterminal">$b</span>:expr, <span class="macro-nonterminal">$answer</span>:expr) => { |
| <span class="macro">assert_eq!</span>(<span class="macro-nonterminal">$a </span>- <span class="macro-nonterminal">$b</span>, <span class="macro-nonterminal">$answer</span>); |
| <span class="macro">assert_eq!</span>( |
| { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro-nonterminal">$a</span>; |
| x -= <span class="macro-nonterminal">$b</span>; |
| x |
| }, |
| <span class="macro-nonterminal">$answer |
| </span>); |
| }; |
| (<span class="macro-nonterminal">$a</span>:ident * <span class="macro-nonterminal">$b</span>:expr, <span class="macro-nonterminal">$answer</span>:expr) => { |
| <span class="macro">assert_eq!</span>(<span class="macro-nonterminal">$a </span>* <span class="macro-nonterminal">$b</span>, <span class="macro-nonterminal">$answer</span>); |
| <span class="macro">assert_eq!</span>( |
| { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro-nonterminal">$a</span>; |
| x <span class="kw-2">*</span>= <span class="macro-nonterminal">$b</span>; |
| x |
| }, |
| <span class="macro-nonterminal">$answer |
| </span>); |
| }; |
| (<span class="macro-nonterminal">$a</span>:ident / <span class="macro-nonterminal">$b</span>:expr, <span class="macro-nonterminal">$answer</span>:expr) => { |
| <span class="macro">assert_eq!</span>(<span class="macro-nonterminal">$a </span>/ <span class="macro-nonterminal">$b</span>, <span class="macro-nonterminal">$answer</span>); |
| <span class="macro">assert_eq!</span>( |
| { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro-nonterminal">$a</span>; |
| x /= <span class="macro-nonterminal">$b</span>; |
| x |
| }, |
| <span class="macro-nonterminal">$answer |
| </span>); |
| }; |
| (<span class="macro-nonterminal">$a</span>:ident % <span class="macro-nonterminal">$b</span>:expr, <span class="macro-nonterminal">$answer</span>:expr) => { |
| <span class="macro">assert_eq!</span>(<span class="macro-nonterminal">$a </span>% <span class="macro-nonterminal">$b</span>, <span class="macro-nonterminal">$answer</span>); |
| <span class="macro">assert_eq!</span>( |
| { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = <span class="macro-nonterminal">$a</span>; |
| x %= <span class="macro-nonterminal">$b</span>; |
| x |
| }, |
| <span class="macro-nonterminal">$answer |
| </span>); |
| }; |
| } |
| |
| <span class="comment">// Test both a + b and a + &b |
| </span><span class="macro">macro_rules! </span>test_op { |
| (<span class="macro-nonterminal">$a</span>:ident <span class="macro-nonterminal">$op</span>:tt <span class="macro-nonterminal">$b</span>:expr, <span class="macro-nonterminal">$answer</span>:expr) => { |
| <span class="macro">test_a_op_b!</span>(<span class="macro-nonterminal">$a $op $b</span>, <span class="macro-nonterminal">$answer</span>); |
| <span class="macro">test_a_op_b!</span>(<span class="macro-nonterminal">$a $op </span><span class="kw-2">&</span><span class="macro-nonterminal">$b</span>, <span class="macro-nonterminal">$answer</span>); |
| }; |
| } |
| |
| <span class="kw">mod </span>complex_arithmetic { |
| <span class="kw">use super</span>::{_05_05i, _0_0i, _0_1i, _1_0i, _1_1i, _4_2i, _neg1_1i, all_consts}; |
| <span class="kw">use </span>num_traits::{MulAdd, MulAddAssign, Zero}; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_add() { |
| <span class="macro">test_op!</span>(_05_05i + _05_05i, _1_1i); |
| <span class="macro">test_op!</span>(_0_1i + _1_0i, _1_1i); |
| <span class="macro">test_op!</span>(_1_0i + _neg1_1i, _0_1i); |
| |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="macro">test_op!</span>(_0_0i + c, c); |
| <span class="macro">test_op!</span>(c + _0_0i, c); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_sub() { |
| <span class="macro">test_op!</span>(_05_05i - _05_05i, _0_0i); |
| <span class="macro">test_op!</span>(_0_1i - _1_0i, _neg1_1i); |
| <span class="macro">test_op!</span>(_0_1i - _neg1_1i, _1_0i); |
| |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="macro">test_op!</span>(c - _0_0i, c); |
| <span class="macro">test_op!</span>(c - c, _0_0i); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_mul() { |
| <span class="macro">test_op!</span>(_05_05i * _05_05i, _0_1i.unscale(<span class="number">2.0</span>)); |
| <span class="macro">test_op!</span>(_1_1i * _0_1i, _neg1_1i); |
| |
| <span class="comment">// i^2 & i^4 |
| </span><span class="macro">test_op!</span>(_0_1i * _0_1i, -_1_0i); |
| <span class="macro">assert_eq!</span>(_0_1i * _0_1i * _0_1i * _0_1i, _1_0i); |
| |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="macro">test_op!</span>(c * _1_0i, c); |
| <span class="macro">test_op!</span>(_1_0i * c, c); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| #[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))] |
| </span><span class="kw">fn </span>test_mul_add_float() { |
| <span class="macro">assert_eq!</span>(_05_05i.mul_add(_05_05i, _0_0i), _05_05i * _05_05i + _0_0i); |
| <span class="macro">assert_eq!</span>(_05_05i * _05_05i + _0_0i, _05_05i.mul_add(_05_05i, _0_0i)); |
| <span class="macro">assert_eq!</span>(_0_1i.mul_add(_0_1i, _0_1i), _neg1_1i); |
| <span class="macro">assert_eq!</span>(_1_0i.mul_add(_1_0i, _1_0i), _1_0i * _1_0i + _1_0i); |
| <span class="macro">assert_eq!</span>(_1_0i * _1_0i + _1_0i, _1_0i.mul_add(_1_0i, _1_0i)); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>x = _1_0i; |
| x.mul_add_assign(_1_0i, _1_0i); |
| <span class="macro">assert_eq!</span>(x, _1_0i * _1_0i + _1_0i); |
| |
| <span class="kw">for </span><span class="kw-2">&</span>a <span class="kw">in </span><span class="kw-2">&</span>all_consts { |
| <span class="kw">for </span><span class="kw-2">&</span>b <span class="kw">in </span><span class="kw-2">&</span>all_consts { |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span><span class="kw-2">&</span>all_consts { |
| <span class="kw">let </span>abc = a * b + c; |
| <span class="macro">assert_eq!</span>(a.mul_add(b, c), abc); |
| <span class="kw">let </span><span class="kw-2">mut </span>x = a; |
| x.mul_add_assign(b, c); |
| <span class="macro">assert_eq!</span>(x, abc); |
| } |
| } |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_mul_add() { |
| <span class="kw">use </span><span class="kw">super</span>::Complex; |
| <span class="kw">const </span>_0_0i: Complex<i32> = Complex { re: <span class="number">0</span>, im: <span class="number">0 </span>}; |
| <span class="kw">const </span>_1_0i: Complex<i32> = Complex { re: <span class="number">1</span>, im: <span class="number">0 </span>}; |
| <span class="kw">const </span>_1_1i: Complex<i32> = Complex { re: <span class="number">1</span>, im: <span class="number">1 </span>}; |
| <span class="kw">const </span>_0_1i: Complex<i32> = Complex { re: <span class="number">0</span>, im: <span class="number">1 </span>}; |
| <span class="kw">const </span>_neg1_1i: Complex<i32> = Complex { re: -<span class="number">1</span>, im: <span class="number">1 </span>}; |
| <span class="kw">const </span>all_consts: [Complex<i32>; <span class="number">5</span>] = [_0_0i, _1_0i, _1_1i, _0_1i, _neg1_1i]; |
| |
| <span class="macro">assert_eq!</span>(_1_0i.mul_add(_1_0i, _0_0i), _1_0i * _1_0i + _0_0i); |
| <span class="macro">assert_eq!</span>(_1_0i * _1_0i + _0_0i, _1_0i.mul_add(_1_0i, _0_0i)); |
| <span class="macro">assert_eq!</span>(_0_1i.mul_add(_0_1i, _0_1i), _neg1_1i); |
| <span class="macro">assert_eq!</span>(_1_0i.mul_add(_1_0i, _1_0i), _1_0i * _1_0i + _1_0i); |
| <span class="macro">assert_eq!</span>(_1_0i * _1_0i + _1_0i, _1_0i.mul_add(_1_0i, _1_0i)); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>x = _1_0i; |
| x.mul_add_assign(_1_0i, _1_0i); |
| <span class="macro">assert_eq!</span>(x, _1_0i * _1_0i + _1_0i); |
| |
| <span class="kw">for </span><span class="kw-2">&</span>a <span class="kw">in </span><span class="kw-2">&</span>all_consts { |
| <span class="kw">for </span><span class="kw-2">&</span>b <span class="kw">in </span><span class="kw-2">&</span>all_consts { |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span><span class="kw-2">&</span>all_consts { |
| <span class="kw">let </span>abc = a * b + c; |
| <span class="macro">assert_eq!</span>(a.mul_add(b, c), abc); |
| <span class="kw">let </span><span class="kw-2">mut </span>x = a; |
| x.mul_add_assign(b, c); |
| <span class="macro">assert_eq!</span>(x, abc); |
| } |
| } |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_div() { |
| <span class="macro">test_op!</span>(_neg1_1i / _0_1i, _1_1i); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="kw">if </span>c != Zero::zero() { |
| <span class="macro">test_op!</span>(c / c, _1_0i); |
| } |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_rem() { |
| <span class="macro">test_op!</span>(_neg1_1i % _0_1i, _0_0i); |
| <span class="macro">test_op!</span>(_4_2i % _0_1i, _0_0i); |
| <span class="macro">test_op!</span>(_05_05i % _0_1i, _05_05i); |
| <span class="macro">test_op!</span>(_05_05i % _1_1i, _05_05i); |
| <span class="macro">assert_eq!</span>((_4_2i + _05_05i) % _0_1i, _05_05i); |
| <span class="macro">assert_eq!</span>((_4_2i + _05_05i) % _1_1i, _05_05i); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_neg() { |
| <span class="macro">assert_eq!</span>(-_1_0i + _0_1i, _neg1_1i); |
| <span class="macro">assert_eq!</span>((-_0_1i) * _0_1i, _1_0i); |
| <span class="kw">for </span><span class="kw-2">&</span>c <span class="kw">in </span>all_consts.iter() { |
| <span class="macro">assert_eq!</span>(-(-c), c); |
| } |
| } |
| } |
| |
| <span class="kw">mod </span>real_arithmetic { |
| <span class="kw">use </span><span class="kw">super</span>::<span class="kw">super</span>::Complex; |
| <span class="kw">use super</span>::{_4_2i, _neg1_1i}; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_add() { |
| <span class="macro">test_op!</span>(_4_2i + <span class="number">0.5</span>, Complex::new(<span class="number">4.5</span>, <span class="number">2.0</span>)); |
| <span class="macro">assert_eq!</span>(<span class="number">0.5 </span>+ _4_2i, Complex::new(<span class="number">4.5</span>, <span class="number">2.0</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_sub() { |
| <span class="macro">test_op!</span>(_4_2i - <span class="number">0.5</span>, Complex::new(<span class="number">3.5</span>, <span class="number">2.0</span>)); |
| <span class="macro">assert_eq!</span>(<span class="number">0.5 </span>- _4_2i, Complex::new(-<span class="number">3.5</span>, -<span class="number">2.0</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_mul() { |
| <span class="macro">assert_eq!</span>(_4_2i * <span class="number">0.5</span>, Complex::new(<span class="number">2.0</span>, <span class="number">1.0</span>)); |
| <span class="macro">assert_eq!</span>(<span class="number">0.5 </span>* _4_2i, Complex::new(<span class="number">2.0</span>, <span class="number">1.0</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_div() { |
| <span class="macro">assert_eq!</span>(_4_2i / <span class="number">0.5</span>, Complex::new(<span class="number">8.0</span>, <span class="number">4.0</span>)); |
| <span class="macro">assert_eq!</span>(<span class="number">0.5 </span>/ _4_2i, Complex::new(<span class="number">0.1</span>, -<span class="number">0.05</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_rem() { |
| <span class="macro">assert_eq!</span>(_4_2i % <span class="number">2.0</span>, Complex::new(<span class="number">0.0</span>, <span class="number">0.0</span>)); |
| <span class="macro">assert_eq!</span>(_4_2i % <span class="number">3.0</span>, Complex::new(<span class="number">1.0</span>, <span class="number">2.0</span>)); |
| <span class="macro">assert_eq!</span>(<span class="number">3.0 </span>% _4_2i, Complex::new(<span class="number">3.0</span>, <span class="number">0.0</span>)); |
| <span class="macro">assert_eq!</span>(_neg1_1i % <span class="number">2.0</span>, _neg1_1i); |
| <span class="macro">assert_eq!</span>(-_4_2i % <span class="number">3.0</span>, Complex::new(-<span class="number">1.0</span>, -<span class="number">2.0</span>)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_div_rem_gaussian() { |
| <span class="comment">// These would overflow with `norm_sqr` division. |
| </span><span class="kw">let </span>max = Complex::new(<span class="number">255u8</span>, <span class="number">255u8</span>); |
| <span class="macro">assert_eq!</span>(max / <span class="number">200</span>, Complex::new(<span class="number">1</span>, <span class="number">1</span>)); |
| <span class="macro">assert_eq!</span>(max % <span class="number">200</span>, Complex::new(<span class="number">55</span>, <span class="number">55</span>)); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_to_string() { |
| <span class="kw">fn </span>test(c: Complex64, s: String) { |
| <span class="macro">assert_eq!</span>(c.to_string(), s); |
| } |
| test(_0_0i, <span class="string">"0+0i"</span>.to_string()); |
| test(_1_0i, <span class="string">"1+0i"</span>.to_string()); |
| test(_0_1i, <span class="string">"0+1i"</span>.to_string()); |
| test(_1_1i, <span class="string">"1+1i"</span>.to_string()); |
| test(_neg1_1i, <span class="string">"-1+1i"</span>.to_string()); |
| test(-_neg1_1i, <span class="string">"1-1i"</span>.to_string()); |
| test(_05_05i, <span class="string">"0.5+0.5i"</span>.to_string()); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_string_formatting() { |
| <span class="kw">let </span>a = Complex::new(<span class="number">1.23456</span>, <span class="number">123.456</span>); |
| <span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{}"</span>, a), <span class="string">"1.23456+123.456i"</span>); |
| <span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:.2}"</span>, a), <span class="string">"1.23+123.46i"</span>); |
| <span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:.2e}"</span>, a), <span class="string">"1.23e0+1.23e2i"</span>); |
| <span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:+.2E}"</span>, a), <span class="string">"+1.23E0+1.23E2i"</span>); |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| </span><span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:+20.2E}"</span>, a), <span class="string">" +1.23E0+1.23E2i"</span>); |
| |
| <span class="kw">let </span>b = Complex::new(<span class="number">0x80</span>, <span class="number">0xff</span>); |
| <span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:X}"</span>, b), <span class="string">"80+FFi"</span>); |
| <span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:#x}"</span>, b), <span class="string">"0x80+0xffi"</span>); |
| <span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:+#b}"</span>, b), <span class="string">"+0b10000000+0b11111111i"</span>); |
| <span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:+#o}"</span>, b), <span class="string">"+0o200+0o377i"</span>); |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| </span><span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:+#16o}"</span>, b), <span class="string">" +0o200+0o377i"</span>); |
| |
| <span class="kw">let </span>c = Complex::new(-<span class="number">10</span>, -<span class="number">10000</span>); |
| <span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{}"</span>, c), <span class="string">"-10-10000i"</span>); |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| </span><span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:16}"</span>, c), <span class="string">" -10-10000i"</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_hash() { |
| <span class="kw">let </span>a = Complex::new(<span class="number">0i32</span>, <span class="number">0i32</span>); |
| <span class="kw">let </span>b = Complex::new(<span class="number">1i32</span>, <span class="number">0i32</span>); |
| <span class="kw">let </span>c = Complex::new(<span class="number">0i32</span>, <span class="number">1i32</span>); |
| <span class="macro">assert!</span>(<span class="kw">crate</span>::hash(<span class="kw-2">&</span>a) != <span class="kw">crate</span>::hash(<span class="kw-2">&</span>b)); |
| <span class="macro">assert!</span>(<span class="kw">crate</span>::hash(<span class="kw-2">&</span>b) != <span class="kw">crate</span>::hash(<span class="kw-2">&</span>c)); |
| <span class="macro">assert!</span>(<span class="kw">crate</span>::hash(<span class="kw-2">&</span>c) != <span class="kw">crate</span>::hash(<span class="kw-2">&</span>a)); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_hashset() { |
| <span class="kw">use </span>std::collections::HashSet; |
| <span class="kw">let </span>a = Complex::new(<span class="number">0i32</span>, <span class="number">0i32</span>); |
| <span class="kw">let </span>b = Complex::new(<span class="number">1i32</span>, <span class="number">0i32</span>); |
| <span class="kw">let </span>c = Complex::new(<span class="number">0i32</span>, <span class="number">1i32</span>); |
| |
| <span class="kw">let </span>set: HashSet<<span class="kw">_</span>> = [a, b, c].iter().cloned().collect(); |
| <span class="macro">assert!</span>(set.contains(<span class="kw-2">&</span>a)); |
| <span class="macro">assert!</span>(set.contains(<span class="kw-2">&</span>b)); |
| <span class="macro">assert!</span>(set.contains(<span class="kw-2">&</span>c)); |
| <span class="macro">assert!</span>(!set.contains(<span class="kw-2">&</span>(a + b + c))); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_is_nan() { |
| <span class="macro">assert!</span>(!_1_1i.is_nan()); |
| <span class="kw">let </span>a = Complex::new(f64::NAN, f64::NAN); |
| <span class="macro">assert!</span>(a.is_nan()); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_is_nan_special_cases() { |
| <span class="kw">let </span>a = Complex::new(<span class="number">0f64</span>, f64::NAN); |
| <span class="kw">let </span>b = Complex::new(f64::NAN, <span class="number">0f64</span>); |
| <span class="macro">assert!</span>(a.is_nan()); |
| <span class="macro">assert!</span>(b.is_nan()); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_is_infinite() { |
| <span class="kw">let </span>a = Complex::new(<span class="number">2f64</span>, f64::INFINITY); |
| <span class="macro">assert!</span>(a.is_infinite()); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_is_finite() { |
| <span class="macro">assert!</span>(_1_1i.is_finite()) |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_is_normal() { |
| <span class="kw">let </span>a = Complex::new(<span class="number">0f64</span>, f64::NAN); |
| <span class="kw">let </span>b = Complex::new(<span class="number">2f64</span>, f64::INFINITY); |
| <span class="macro">assert!</span>(!a.is_normal()); |
| <span class="macro">assert!</span>(!b.is_normal()); |
| <span class="macro">assert!</span>(_1_1i.is_normal()); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_from_str() { |
| <span class="kw">fn </span>test(z: Complex64, s: <span class="kw-2">&</span>str) { |
| <span class="macro">assert_eq!</span>(FromStr::from_str(s), <span class="prelude-val">Ok</span>(z)); |
| } |
| test(_0_0i, <span class="string">"0 + 0i"</span>); |
| test(_0_0i, <span class="string">"0+0j"</span>); |
| test(_0_0i, <span class="string">"0 - 0j"</span>); |
| test(_0_0i, <span class="string">"0-0i"</span>); |
| test(_0_0i, <span class="string">"0i + 0"</span>); |
| test(_0_0i, <span class="string">"0"</span>); |
| test(_0_0i, <span class="string">"-0"</span>); |
| test(_0_0i, <span class="string">"0i"</span>); |
| test(_0_0i, <span class="string">"0j"</span>); |
| test(_0_0i, <span class="string">"+0j"</span>); |
| test(_0_0i, <span class="string">"-0i"</span>); |
| |
| test(_1_0i, <span class="string">"1 + 0i"</span>); |
| test(_1_0i, <span class="string">"1+0j"</span>); |
| test(_1_0i, <span class="string">"1 - 0j"</span>); |
| test(_1_0i, <span class="string">"+1-0i"</span>); |
| test(_1_0i, <span class="string">"-0j+1"</span>); |
| test(_1_0i, <span class="string">"1"</span>); |
| |
| test(_1_1i, <span class="string">"1 + i"</span>); |
| test(_1_1i, <span class="string">"1+j"</span>); |
| test(_1_1i, <span class="string">"1 + 1j"</span>); |
| test(_1_1i, <span class="string">"1+1i"</span>); |
| test(_1_1i, <span class="string">"i + 1"</span>); |
| test(_1_1i, <span class="string">"1i+1"</span>); |
| test(_1_1i, <span class="string">"+j+1"</span>); |
| |
| test(_0_1i, <span class="string">"0 + i"</span>); |
| test(_0_1i, <span class="string">"0+j"</span>); |
| test(_0_1i, <span class="string">"-0 + j"</span>); |
| test(_0_1i, <span class="string">"-0+i"</span>); |
| test(_0_1i, <span class="string">"0 + 1i"</span>); |
| test(_0_1i, <span class="string">"0+1j"</span>); |
| test(_0_1i, <span class="string">"-0 + 1j"</span>); |
| test(_0_1i, <span class="string">"-0+1i"</span>); |
| test(_0_1i, <span class="string">"j + 0"</span>); |
| test(_0_1i, <span class="string">"i"</span>); |
| test(_0_1i, <span class="string">"j"</span>); |
| test(_0_1i, <span class="string">"1j"</span>); |
| |
| test(_neg1_1i, <span class="string">"-1 + i"</span>); |
| test(_neg1_1i, <span class="string">"-1+j"</span>); |
| test(_neg1_1i, <span class="string">"-1 + 1j"</span>); |
| test(_neg1_1i, <span class="string">"-1+1i"</span>); |
| test(_neg1_1i, <span class="string">"1i-1"</span>); |
| test(_neg1_1i, <span class="string">"j + -1"</span>); |
| |
| test(_05_05i, <span class="string">"0.5 + 0.5i"</span>); |
| test(_05_05i, <span class="string">"0.5+0.5j"</span>); |
| test(_05_05i, <span class="string">"5e-1+0.5j"</span>); |
| test(_05_05i, <span class="string">"5E-1 + 0.5j"</span>); |
| test(_05_05i, <span class="string">"5E-1i + 0.5"</span>); |
| test(_05_05i, <span class="string">"0.05e+1j + 50E-2"</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_from_str_radix() { |
| <span class="kw">fn </span>test(z: Complex64, s: <span class="kw-2">&</span>str, radix: u32) { |
| <span class="kw">let </span>res: <span class="prelude-ty">Result</span><Complex64, <Complex64 <span class="kw">as </span>Num>::FromStrRadixErr> = |
| Num::from_str_radix(s, radix); |
| <span class="macro">assert_eq!</span>(res.unwrap(), z) |
| } |
| test(_4_2i, <span class="string">"4+2i"</span>, <span class="number">10</span>); |
| test(Complex::new(<span class="number">15.0</span>, <span class="number">32.0</span>), <span class="string">"F+20i"</span>, <span class="number">16</span>); |
| test(Complex::new(<span class="number">15.0</span>, <span class="number">32.0</span>), <span class="string">"1111+100000i"</span>, <span class="number">2</span>); |
| test(Complex::new(-<span class="number">15.0</span>, -<span class="number">32.0</span>), <span class="string">"-F-20i"</span>, <span class="number">16</span>); |
| test(Complex::new(-<span class="number">15.0</span>, -<span class="number">32.0</span>), <span class="string">"-1111-100000i"</span>, <span class="number">2</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_from_str_fail() { |
| <span class="kw">fn </span>test(s: <span class="kw-2">&</span>str) { |
| <span class="kw">let </span>complex: <span class="prelude-ty">Result</span><Complex64, <span class="kw">_</span>> = FromStr::from_str(s); |
| <span class="macro">assert!</span>( |
| complex.is_err(), |
| <span class="string">"complex {:?} -> {:?} should be an error"</span>, |
| s, |
| complex |
| ); |
| } |
| test(<span class="string">"foo"</span>); |
| test(<span class="string">"6E"</span>); |
| test(<span class="string">"0 + 2.718"</span>); |
| test(<span class="string">"1 - -2i"</span>); |
| test(<span class="string">"314e-2ij"</span>); |
| test(<span class="string">"4.3j - i"</span>); |
| test(<span class="string">"1i - 2i"</span>); |
| test(<span class="string">"+ 1 - 3.0i"</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_sum() { |
| <span class="kw">let </span>v = <span class="macro">vec!</span>[_0_1i, _1_0i]; |
| <span class="macro">assert_eq!</span>(v.iter().sum::<Complex64>(), _1_1i); |
| <span class="macro">assert_eq!</span>(v.into_iter().sum::<Complex64>(), _1_1i); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_prod() { |
| <span class="kw">let </span>v = <span class="macro">vec!</span>[_0_1i, _1_0i]; |
| <span class="macro">assert_eq!</span>(v.iter().product::<Complex64>(), _0_1i); |
| <span class="macro">assert_eq!</span>(v.into_iter().product::<Complex64>(), _0_1i); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_zero() { |
| <span class="kw">let </span>zero = Complex64::zero(); |
| <span class="macro">assert!</span>(zero.is_zero()); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>c = Complex::new(<span class="number">1.23</span>, <span class="number">4.56</span>); |
| <span class="macro">assert!</span>(!c.is_zero()); |
| <span class="macro">assert_eq!</span>(c + zero, c); |
| |
| c.set_zero(); |
| <span class="macro">assert!</span>(c.is_zero()); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_one() { |
| <span class="kw">let </span>one = Complex64::one(); |
| <span class="macro">assert!</span>(one.is_one()); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>c = Complex::new(<span class="number">1.23</span>, <span class="number">4.56</span>); |
| <span class="macro">assert!</span>(!c.is_one()); |
| <span class="macro">assert_eq!</span>(c * one, c); |
| |
| c.set_one(); |
| <span class="macro">assert!</span>(c.is_one()); |
| } |
| |
| <span class="attribute">#[test] |
| #[allow(clippy::float_cmp)] |
| </span><span class="kw">fn </span>test_const() { |
| <span class="kw">const </span>R: f64 = <span class="number">12.3</span>; |
| <span class="kw">const </span>I: f64 = -<span class="number">4.5</span>; |
| <span class="kw">const </span>C: Complex64 = Complex::new(R, I); |
| |
| <span class="macro">assert_eq!</span>(C.re, <span class="number">12.3</span>); |
| <span class="macro">assert_eq!</span>(C.im, -<span class="number">4.5</span>); |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="num_complex" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |