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</pre><pre class="rust">
<span class="comment">// Copyright 2013 The Rust Project Developers. See the COPYRIGHT</span>
<span class="comment">// file at the top-level directory of this distribution and at</span>
<span class="comment">// http://rust-lang.org/COPYRIGHT.</span>
<span class="comment">//</span>
<span class="comment">// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or</span>
<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license</span>
<span class="comment">// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your</span>
<span class="comment">// option. This file may not be copied, modified, or distributed</span>
<span class="comment">// except according to those terms.</span>
<span class="doccomment">//! Complex numbers.</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! ## Compatibility</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! The `num-complex` crate is tested for rustc 1.8 and greater.</span>
<span class="attribute">#![<span class="ident">doc</span>(<span class="ident">html_root_url</span> <span class="op">=</span> <span class="string">"https://docs.rs/num-complex/0.1"</span>)]</span>
<span class="kw">extern</span> <span class="kw">crate</span> <span class="ident">num_traits</span> <span class="kw">as</span> <span class="ident">traits</span>;
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"rustc-serialize"</span>)]</span>
<span class="kw">extern</span> <span class="kw">crate</span> <span class="ident">rustc_serialize</span>;
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"serde"</span>)]</span>
<span class="kw">extern</span> <span class="kw">crate</span> <span class="ident">serde</span>;
<span class="kw">use</span> <span class="ident">std::error::Error</span>;
<span class="kw">use</span> <span class="ident">std::fmt</span>;
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">use</span> <span class="ident">std::hash</span>;
<span class="kw">use</span> <span class="ident">std::ops</span>::{<span class="ident">Add</span>, <span class="ident">Div</span>, <span class="ident">Mul</span>, <span class="ident">Neg</span>, <span class="ident">Sub</span>, <span class="ident">Rem</span>};
<span class="kw">use</span> <span class="ident">std::str::FromStr</span>;
<span class="kw">use</span> <span class="ident">traits</span>::{<span class="ident">Zero</span>, <span class="ident">One</span>, <span class="ident">Num</span>, <span class="ident">Float</span>};
<span class="comment">// FIXME #1284: handle complex NaN & infinity etc. This</span>
<span class="comment">// probably doesn't map to C's _Complex correctly.</span>
<span class="doccomment">/// A complex number in Cartesian form.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ## Representation and Foreign Function Interface Compatibility</span>
<span class="doccomment">///</span>
<span class="doccomment">/// `Complex<T>` is memory layout compatible with an array `[T; 2]`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Note that `Complex<F>` where F is a floating point type is **only** memory</span>
<span class="doccomment">/// layout compatible with C's complex types, **not** necessarily calling</span>
<span class="doccomment">/// convention compatible. This means that for FFI you can only pass</span>
<span class="doccomment">/// `Complex<F>` behind a pointer, not as a value.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ## Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Example of extern function declaration.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_complex::Complex;</span>
<span class="doccomment">/// use std::os::raw::c_int;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// extern "C" {</span>
<span class="doccomment">/// fn zaxpy_(n: *const c_int, alpha: *const Complex<f64>,</span>
<span class="doccomment">/// x: *const Complex<f64>, incx: *const c_int,</span>
<span class="doccomment">/// y: *mut Complex<f64>, incy: *const c_int);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">PartialEq</span>, <span class="ident">Eq</span>, <span class="ident">Copy</span>, <span class="ident">Clone</span>, <span class="ident">Hash</span>, <span class="ident">Debug</span>, <span class="ident">Default</span>)]</span>
<span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"rustc-serialize"</span>, <span class="ident">derive</span>(<span class="ident">RustcEncodable</span>, <span class="ident">RustcDecodable</span>))]</span>
<span class="attribute">#[<span class="ident">repr</span>(<span class="ident">C</span>)]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="doccomment">/// Real portion of the complex number</span>
<span class="kw">pub</span> <span class="ident">re</span>: <span class="ident">T</span>,
<span class="doccomment">/// Imaginary portion of the complex number</span>
<span class="kw">pub</span> <span class="ident">im</span>: <span class="ident">T</span>
}
<span class="kw">pub</span> <span class="kw">type</span> <span class="ident">Complex32</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">f32</span><span class="op">></span>;
<span class="kw">pub</span> <span class="kw">type</span> <span class="ident">Complex64</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span>;
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="doccomment">/// Create a new Complex</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">re</span>: <span class="ident">T</span>, <span class="ident">im</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex</span> { <span class="ident">re</span>: <span class="ident">re</span>, <span class="ident">im</span>: <span class="ident">im</span> }
}
<span class="doccomment">/// Returns imaginary unit</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">i</span>() <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="self">Self</span><span class="ident">::new</span>(<span class="ident">T::zero</span>(), <span class="ident">T::one</span>())
}
<span class="doccomment">/// Returns the square of the norm (since `T` doesn't necessarily</span>
<span class="doccomment">/// have a sqrt function), i.e. `re^2 + im^2`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">norm_sqr</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">T</span> {
<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">clone</span>() <span class="op">*</span> <span class="self">self</span>.<span class="ident">re</span>.<span class="ident">clone</span>() <span class="op">+</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">clone</span>() <span class="op">*</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">clone</span>()
}
<span class="doccomment">/// Multiplies `self` by the scalar `t`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">scale</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">t</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">clone</span>() <span class="op">*</span> <span class="ident">t</span>.<span class="ident">clone</span>(), <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">clone</span>() <span class="op">*</span> <span class="ident">t</span>)
}
<span class="doccomment">/// Divides `self` by the scalar `t`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">unscale</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">t</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">clone</span>() <span class="op">/</span> <span class="ident">t</span>.<span class="ident">clone</span>(), <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">clone</span>() <span class="op">/</span> <span class="ident">t</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">Neg</span><span class="op"><</span><span class="ident">Output</span> <span class="op">=</span> <span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="doccomment">/// Returns the complex conjugate. i.e. `re - i im`</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">conj</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">clone</span>(), <span class="op">-</span><span class="self">self</span>.<span class="ident">im</span>.<span class="ident">clone</span>())
}
<span class="doccomment">/// Returns `1/self`</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">inv</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">let</span> <span class="ident">norm_sqr</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">norm_sqr</span>();
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">clone</span>() <span class="op">/</span> <span class="ident">norm_sqr</span>.<span class="ident">clone</span>(),
<span class="op">-</span><span class="self">self</span>.<span class="ident">im</span>.<span class="ident">clone</span>() <span class="op">/</span> <span class="ident">norm_sqr</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Float</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="doccomment">/// Calculate |self|</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">norm</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">T</span> {
<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">hypot</span>(<span class="self">self</span>.<span class="ident">im</span>)
}
<span class="doccomment">/// Calculate the principal Arg of self.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">arg</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">T</span> {
<span class="self">self</span>.<span class="ident">im</span>.<span class="ident">atan2</span>(<span class="self">self</span>.<span class="ident">re</span>)
}
<span class="doccomment">/// Convert to polar form (r, theta), such that</span>
<span class="doccomment">/// `self = r * exp(i * theta)`</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">to_polar</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> (<span class="ident">T</span>, <span class="ident">T</span>) {
(<span class="self">self</span>.<span class="ident">norm</span>(), <span class="self">self</span>.<span class="ident">arg</span>())
}
<span class="doccomment">/// Convert a polar representation into a complex number.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">from_polar</span>(<span class="ident">r</span>: <span class="kw-2">&</span><span class="ident">T</span>, <span class="ident">theta</span>: <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="kw-2">*</span><span class="ident">r</span> <span class="op">*</span> <span class="ident">theta</span>.<span class="ident">cos</span>(), <span class="kw-2">*</span><span class="ident">r</span> <span class="op">*</span> <span class="ident">theta</span>.<span class="ident">sin</span>())
}
<span class="doccomment">/// Computes `e^(self)`, where `e` is the base of the natural logarithm.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">exp</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: e^(a + bi) = e^a (cos(b) + i*sin(b))</span>
<span class="comment">// = from_polar(e^a, b)</span>
<span class="ident">Complex::from_polar</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">re</span>.<span class="ident">exp</span>(), <span class="kw-2">&</span><span class="self">self</span>.<span class="ident">im</span>)
}
<span class="doccomment">/// Computes the principal value of natural logarithm of `self`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This function has one branch cut:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * `(-∞, 0]`, continuous from above.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The branch satisfies `-π ≤ arg(ln(z)) ≤ π`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">ln</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: ln(z) = ln|z| + i*arg(z)</span>
<span class="kw">let</span> (<span class="ident">r</span>, <span class="ident">theta</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">to_polar</span>();
<span class="ident">Complex::new</span>(<span class="ident">r</span>.<span class="ident">ln</span>(), <span class="ident">theta</span>)
}
<span class="doccomment">/// Computes the principal value of the square root of `self`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This function has one branch cut:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * `(-∞, 0)`, continuous from above.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The branch satisfies `-π/2 ≤ arg(sqrt(z)) ≤ π/2`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">sqrt</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: sqrt(r e^(it)) = sqrt(r) e^(it/2)</span>
<span class="kw">let</span> <span class="ident">two</span> <span class="op">=</span> <span class="ident">T::one</span>() <span class="op">+</span> <span class="ident">T::one</span>();
<span class="kw">let</span> (<span class="ident">r</span>, <span class="ident">theta</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">to_polar</span>();
<span class="ident">Complex::from_polar</span>(<span class="kw-2">&</span>(<span class="ident">r</span>.<span class="ident">sqrt</span>()), <span class="kw-2">&</span>(<span class="ident">theta</span><span class="op">/</span><span class="ident">two</span>))
}
<span class="doccomment">/// Raises `self` to a floating point power.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">powf</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">exp</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: x^y = (ρ e^(i θ))^y = ρ^y e^(i θ y)</span>
<span class="comment">// = from_polar(ρ^y, θ y)</span>
<span class="kw">let</span> (<span class="ident">r</span>, <span class="ident">theta</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">to_polar</span>();
<span class="ident">Complex::from_polar</span>(<span class="kw-2">&</span><span class="ident">r</span>.<span class="ident">powf</span>(<span class="ident">exp</span>), <span class="kw-2">&</span>(<span class="ident">theta</span><span class="kw-2">*</span><span class="ident">exp</span>))
}
<span class="doccomment">/// Returns the logarithm of `self` with respect to an arbitrary base.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">log</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">base</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: log_y(x) = log_y(ρ e^(i θ))</span>
<span class="comment">// = log_y(ρ) + log_y(e^(i θ)) = log_y(ρ) + ln(e^(i θ)) / ln(y)</span>
<span class="comment">// = log_y(ρ) + i θ / ln(y)</span>
<span class="kw">let</span> (<span class="ident">r</span>, <span class="ident">theta</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">to_polar</span>();
<span class="ident">Complex::new</span>(<span class="ident">r</span>.<span class="ident">log</span>(<span class="ident">base</span>), <span class="ident">theta</span> <span class="op">/</span> <span class="ident">base</span>.<span class="ident">ln</span>())
}
<span class="doccomment">/// Raises `self` to a complex power.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">powc</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">exp</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: x^y = (a + i b)^(c + i d)</span>
<span class="comment">// = (ρ e^(i θ))^c (ρ e^(i θ))^(i d)</span>
<span class="comment">// where ρ=|x| and θ=arg(x)</span>
<span class="comment">// = ρ^c e^(−d θ) e^(i c θ) ρ^(i d)</span>
<span class="comment">// = p^c e^(−d θ) (cos(c θ)</span>
<span class="comment">// + i sin(c θ)) (cos(d ln(ρ)) + i sin(d ln(ρ)))</span>
<span class="comment">// = p^c e^(−d θ) (</span>
<span class="comment">// cos(c θ) cos(d ln(ρ)) − sin(c θ) sin(d ln(ρ))</span>
<span class="comment">// + i(cos(c θ) sin(d ln(ρ)) + sin(c θ) cos(d ln(ρ))))</span>
<span class="comment">// = p^c e^(−d θ) (cos(c θ + d ln(ρ)) + i sin(c θ + d ln(ρ)))</span>
<span class="comment">// = from_polar(p^c e^(−d θ), c θ + d ln(ρ))</span>
<span class="kw">let</span> (<span class="ident">r</span>, <span class="ident">theta</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">to_polar</span>();
<span class="ident">Complex::from_polar</span>(
<span class="kw-2">&</span>(<span class="ident">r</span>.<span class="ident">powf</span>(<span class="ident">exp</span>.<span class="ident">re</span>) <span class="op">*</span> (<span class="op">-</span><span class="ident">exp</span>.<span class="ident">im</span> <span class="op">*</span> <span class="ident">theta</span>).<span class="ident">exp</span>()),
<span class="kw-2">&</span>(<span class="ident">exp</span>.<span class="ident">re</span> <span class="op">*</span> <span class="ident">theta</span> <span class="op">+</span> <span class="ident">exp</span>.<span class="ident">im</span> <span class="op">*</span> <span class="ident">r</span>.<span class="ident">ln</span>()))
}
<span class="doccomment">/// Raises a floating point number to the complex power `self`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">expf</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">base</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: x^(a+bi) = x^a x^bi = x^a e^(b ln(x) i)</span>
<span class="comment">// = from_polar(x^a, b ln(x))</span>
<span class="ident">Complex::from_polar</span>(<span class="kw-2">&</span><span class="ident">base</span>.<span class="ident">powf</span>(<span class="self">self</span>.<span class="ident">re</span>), <span class="kw-2">&</span>(<span class="self">self</span>.<span class="ident">im</span> <span class="op">*</span> <span class="ident">base</span>.<span class="ident">ln</span>()))
}
<span class="doccomment">/// Computes the sine of `self`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">sin</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: sin(a + bi) = sin(a)cosh(b) + i*cos(a)sinh(b)</span>
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">sin</span>() <span class="op">*</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">cosh</span>(), <span class="self">self</span>.<span class="ident">re</span>.<span class="ident">cos</span>() <span class="op">*</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">sinh</span>())
}
<span class="doccomment">/// Computes the cosine of `self`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">cos</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: cos(a + bi) = cos(a)cosh(b) - i*sin(a)sinh(b)</span>
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">cos</span>() <span class="op">*</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">cosh</span>(), <span class="op">-</span><span class="self">self</span>.<span class="ident">re</span>.<span class="ident">sin</span>() <span class="op">*</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">sinh</span>())
}
<span class="doccomment">/// Computes the tangent of `self`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">tan</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: tan(a + bi) = (sin(2a) + i*sinh(2b))/(cos(2a) + cosh(2b))</span>
<span class="kw">let</span> (<span class="ident">two_re</span>, <span class="ident">two_im</span>) <span class="op">=</span> (<span class="self">self</span>.<span class="ident">re</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">im</span>);
<span class="ident">Complex::new</span>(<span class="ident">two_re</span>.<span class="ident">sin</span>(), <span class="ident">two_im</span>.<span class="ident">sinh</span>()).<span class="ident">unscale</span>(<span class="ident">two_re</span>.<span class="ident">cos</span>() <span class="op">+</span> <span class="ident">two_im</span>.<span class="ident">cosh</span>())
}
<span class="doccomment">/// Computes the principal value of the inverse sine of `self`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This function has two branch cuts:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * `(-∞, -1)`, continuous from above.</span>
<span class="doccomment">/// * `(1, ∞)`, continuous from below.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The branch satisfies `-π/2 ≤ Re(asin(z)) ≤ π/2`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">asin</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: arcsin(z) = -i ln(sqrt(1-z^2) + iz)</span>
<span class="kw">let</span> <span class="ident">i</span> <span class="op">=</span> <span class="ident">Complex</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="ident">::i</span>();
<span class="op">-</span><span class="ident">i</span><span class="kw-2">*</span>((<span class="ident">Complex</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="ident">::one</span>() <span class="op">-</span> <span class="self">self</span><span class="kw-2">*</span><span class="self">self</span>).<span class="ident">sqrt</span>() <span class="op">+</span> <span class="ident">i</span><span class="kw-2">*</span><span class="self">self</span>).<span class="ident">ln</span>()
}
<span class="doccomment">/// Computes the principal value of the inverse cosine of `self`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This function has two branch cuts:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * `(-∞, -1)`, continuous from above.</span>
<span class="doccomment">/// * `(1, ∞)`, continuous from below.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The branch satisfies `0 ≤ Re(acos(z)) ≤ π`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">acos</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: arccos(z) = -i ln(i sqrt(1-z^2) + z)</span>
<span class="kw">let</span> <span class="ident">i</span> <span class="op">=</span> <span class="ident">Complex</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="ident">::i</span>();
<span class="op">-</span><span class="ident">i</span><span class="kw-2">*</span>(<span class="ident">i</span><span class="kw-2">*</span>(<span class="ident">Complex</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="ident">::one</span>() <span class="op">-</span> <span class="self">self</span><span class="kw-2">*</span><span class="self">self</span>).<span class="ident">sqrt</span>() <span class="op">+</span> <span class="self">self</span>).<span class="ident">ln</span>()
}
<span class="doccomment">/// Computes the principal value of the inverse tangent of `self`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This function has two branch cuts:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * `(-∞i, -i]`, continuous from the left.</span>
<span class="doccomment">/// * `[i, ∞i)`, continuous from the right.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The branch satisfies `-π/2 ≤ Re(atan(z)) ≤ π/2`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">atan</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: arctan(z) = (ln(1+iz) - ln(1-iz))/(2i)</span>
<span class="kw">let</span> <span class="ident">i</span> <span class="op">=</span> <span class="ident">Complex</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="ident">::i</span>();
<span class="kw">let</span> <span class="ident">one</span> <span class="op">=</span> <span class="ident">Complex</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="ident">::one</span>();
<span class="kw">let</span> <span class="ident">two</span> <span class="op">=</span> <span class="ident">one</span> <span class="op">+</span> <span class="ident">one</span>;
<span class="kw">if</span> <span class="kw-2">*</span><span class="self">self</span> <span class="op">=</span><span class="op">=</span> <span class="ident">i</span> {
<span class="kw">return</span> <span class="ident">Complex::new</span>(<span class="ident">T::zero</span>(), <span class="ident">T::infinity</span>());
}
<span class="kw">else</span> <span class="kw">if</span> <span class="kw-2">*</span><span class="self">self</span> <span class="op">=</span><span class="op">=</span> <span class="op">-</span><span class="ident">i</span> {
<span class="kw">return</span> <span class="ident">Complex::new</span>(<span class="ident">T::zero</span>(), <span class="op">-</span><span class="ident">T::infinity</span>());
}
((<span class="ident">one</span> <span class="op">+</span> <span class="ident">i</span> <span class="op">*</span> <span class="self">self</span>).<span class="ident">ln</span>() <span class="op">-</span> (<span class="ident">one</span> <span class="op">-</span> <span class="ident">i</span> <span class="op">*</span> <span class="self">self</span>).<span class="ident">ln</span>()) <span class="op">/</span> (<span class="ident">two</span> <span class="op">*</span> <span class="ident">i</span>)
}
<span class="doccomment">/// Computes the hyperbolic sine of `self`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">sinh</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: sinh(a + bi) = sinh(a)cos(b) + i*cosh(a)sin(b)</span>
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">sinh</span>() <span class="op">*</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">cos</span>(), <span class="self">self</span>.<span class="ident">re</span>.<span class="ident">cosh</span>() <span class="op">*</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">sin</span>())
}
<span class="doccomment">/// Computes the hyperbolic cosine of `self`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">cosh</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: cosh(a + bi) = cosh(a)cos(b) + i*sinh(a)sin(b)</span>
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">cosh</span>() <span class="op">*</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">cos</span>(), <span class="self">self</span>.<span class="ident">re</span>.<span class="ident">sinh</span>() <span class="op">*</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">sin</span>())
}
<span class="doccomment">/// Computes the hyperbolic tangent of `self`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">tanh</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: tanh(a + bi) = (sinh(2a) + i*sin(2b))/(cosh(2a) + cos(2b))</span>
<span class="kw">let</span> (<span class="ident">two_re</span>, <span class="ident">two_im</span>) <span class="op">=</span> (<span class="self">self</span>.<span class="ident">re</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">im</span>);
<span class="ident">Complex::new</span>(<span class="ident">two_re</span>.<span class="ident">sinh</span>(), <span class="ident">two_im</span>.<span class="ident">sin</span>()).<span class="ident">unscale</span>(<span class="ident">two_re</span>.<span class="ident">cosh</span>() <span class="op">+</span> <span class="ident">two_im</span>.<span class="ident">cos</span>())
}
<span class="doccomment">/// Computes the principal value of inverse hyperbolic sine of `self`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This function has two branch cuts:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * `(-∞i, -i)`, continuous from the left.</span>
<span class="doccomment">/// * `(i, ∞i)`, continuous from the right.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The branch satisfies `-π/2 ≤ Im(asinh(z)) ≤ π/2`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">asinh</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: arcsinh(z) = ln(z + sqrt(1+z^2))</span>
<span class="kw">let</span> <span class="ident">one</span> <span class="op">=</span> <span class="ident">Complex</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="ident">::one</span>();
(<span class="self">self</span> <span class="op">+</span> (<span class="ident">one</span> <span class="op">+</span> <span class="self">self</span> <span class="op">*</span> <span class="self">self</span>).<span class="ident">sqrt</span>()).<span class="ident">ln</span>()
}
<span class="doccomment">/// Computes the principal value of inverse hyperbolic cosine of `self`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This function has one branch cut:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * `(-∞, 1)`, continuous from above.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The branch satisfies `-π ≤ Im(acosh(z)) ≤ π` and `0 ≤ Re(acosh(z)) < ∞`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">acosh</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: arccosh(z) = 2 ln(sqrt((z+1)/2) + sqrt((z-1)/2))</span>
<span class="kw">let</span> <span class="ident">one</span> <span class="op">=</span> <span class="ident">Complex::one</span>();
<span class="kw">let</span> <span class="ident">two</span> <span class="op">=</span> <span class="ident">one</span> <span class="op">+</span> <span class="ident">one</span>;
<span class="ident">two</span> <span class="op">*</span> (((<span class="self">self</span> <span class="op">+</span> <span class="ident">one</span>)<span class="op">/</span><span class="ident">two</span>).<span class="ident">sqrt</span>() <span class="op">+</span> ((<span class="self">self</span> <span class="op">-</span> <span class="ident">one</span>)<span class="op">/</span><span class="ident">two</span>).<span class="ident">sqrt</span>()).<span class="ident">ln</span>()
}
<span class="doccomment">/// Computes the principal value of inverse hyperbolic tangent of `self`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This function has two branch cuts:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * `(-∞, -1]`, continuous from above.</span>
<span class="doccomment">/// * `[1, ∞)`, continuous from below.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The branch satisfies `-π/2 ≤ Im(atanh(z)) ≤ π/2`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">atanh</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="comment">// formula: arctanh(z) = (ln(1+z) - ln(1-z))/2</span>
<span class="kw">let</span> <span class="ident">one</span> <span class="op">=</span> <span class="ident">Complex::one</span>();
<span class="kw">let</span> <span class="ident">two</span> <span class="op">=</span> <span class="ident">one</span> <span class="op">+</span> <span class="ident">one</span>;
<span class="kw">if</span> <span class="kw-2">*</span><span class="self">self</span> <span class="op">=</span><span class="op">=</span> <span class="ident">one</span> {
<span class="kw">return</span> <span class="ident">Complex::new</span>(<span class="ident">T::infinity</span>(), <span class="ident">T::zero</span>());
}
<span class="kw">else</span> <span class="kw">if</span> <span class="kw-2">*</span><span class="self">self</span> <span class="op">=</span><span class="op">=</span> <span class="op">-</span><span class="ident">one</span> {
<span class="kw">return</span> <span class="ident">Complex::new</span>(<span class="op">-</span><span class="ident">T::infinity</span>(), <span class="ident">T::zero</span>());
}
((<span class="ident">one</span> <span class="op">+</span> <span class="self">self</span>).<span class="ident">ln</span>() <span class="op">-</span> (<span class="ident">one</span> <span class="op">-</span> <span class="self">self</span>).<span class="ident">ln</span>()) <span class="op">/</span> <span class="ident">two</span>
}
<span class="doccomment">/// Checks if the given complex number is NaN</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">is_nan</span>(<span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">is_nan</span>() <span class="op">|</span><span class="op">|</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">is_nan</span>()
}
<span class="doccomment">/// Checks if the given complex number is infinite</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">is_infinite</span>(<span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="op">!</span><span class="self">self</span>.<span class="ident">is_nan</span>() <span class="op">&&</span> (<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">is_infinite</span>() <span class="op">|</span><span class="op">|</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">is_infinite</span>())
}
<span class="doccomment">/// Checks if the given complex number is finite</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">is_finite</span>(<span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">is_finite</span>() <span class="op">&&</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">is_finite</span>()
}
<span class="doccomment">/// Checks if the given complex number is normal</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">is_normal</span>(<span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">is_normal</span>() <span class="op">&&</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">is_normal</span>()
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">From</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">from</span>(<span class="ident">re</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex</span> { <span class="ident">re</span>: <span class="ident">re</span>, <span class="ident">im</span>: <span class="ident">T::zero</span>() }
}
}
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">From</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">from</span>(<span class="ident">re</span>: <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">From::from</span>(<span class="ident">re</span>.<span class="ident">clone</span>())
}
}
<span class="macro">macro_rules!</span> <span class="ident">forward_ref_ref_binop</span> {
(<span class="kw">impl</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span>:<span class="ident">ident</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>:<span class="ident">ident</span>) <span class="op">=</span><span class="op">></span> {
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="lifetime">'b</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'b</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="self">self</span>.<span class="ident">clone</span>().<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>.<span class="ident">clone</span>())
}
}
}
}
<span class="macro">macro_rules!</span> <span class="ident">forward_ref_val_binop</span> {
(<span class="kw">impl</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span>:<span class="ident">ident</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>:<span class="ident">ident</span>) <span class="op">=</span><span class="op">></span> {
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="self">self</span>.<span class="ident">clone</span>().<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>)
}
}
}
}
<span class="macro">macro_rules!</span> <span class="ident">forward_val_ref_binop</span> {
(<span class="kw">impl</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span>:<span class="ident">ident</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>:<span class="ident">ident</span>) <span class="op">=</span><span class="op">></span> {
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="self">self</span>.<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>.<span class="ident">clone</span>())
}
}
}
}
<span class="macro">macro_rules!</span> <span class="ident">forward_all_binop</span> {
(<span class="kw">impl</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span>:<span class="ident">ident</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>:<span class="ident">ident</span>) <span class="op">=</span><span class="op">></span> {
<span class="macro">forward_ref_ref_binop!</span>(<span class="kw">impl</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>);
<span class="macro">forward_ref_val_binop!</span>(<span class="kw">impl</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>);
<span class="macro">forward_val_ref_binop!</span>(<span class="kw">impl</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>);
};
}
<span class="comment">/* arithmetic */</span>
<span class="macro">forward_all_binop!</span>(<span class="kw">impl</span> <span class="ident">Add</span>, <span class="ident">add</span>);
<span class="comment">// (a + i b) + (c + i d) == (a + c) + i (b + d)</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Add</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">add</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span> <span class="op">+</span> <span class="ident">other</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span> <span class="op">+</span> <span class="ident">other</span>.<span class="ident">im</span>)
}
}
<span class="macro">forward_all_binop!</span>(<span class="kw">impl</span> <span class="ident">Sub</span>, <span class="ident">sub</span>);
<span class="comment">// (a + i b) - (c + i d) == (a - c) + i (b - d)</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Sub</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">sub</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span> <span class="op">-</span> <span class="ident">other</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span> <span class="op">-</span> <span class="ident">other</span>.<span class="ident">im</span>)
}
}
<span class="macro">forward_all_binop!</span>(<span class="kw">impl</span> <span class="ident">Mul</span>, <span class="ident">mul</span>);
<span class="comment">// (a + i b) * (c + i d) == (a*c - b*d) + i (a*d + b*c)</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Mul</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">mul</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">let</span> <span class="ident">re</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">re</span>.<span class="ident">clone</span>() <span class="op">*</span> <span class="ident">other</span>.<span class="ident">re</span>.<span class="ident">clone</span>() <span class="op">-</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">clone</span>() <span class="op">*</span> <span class="ident">other</span>.<span class="ident">im</span>.<span class="ident">clone</span>();
<span class="kw">let</span> <span class="ident">im</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">re</span> <span class="op">*</span> <span class="ident">other</span>.<span class="ident">im</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">im</span> <span class="op">*</span> <span class="ident">other</span>.<span class="ident">re</span>;
<span class="ident">Complex::new</span>(<span class="ident">re</span>, <span class="ident">im</span>)
}
}
<span class="macro">forward_all_binop!</span>(<span class="kw">impl</span> <span class="ident">Div</span>, <span class="ident">div</span>);
<span class="comment">// (a + i b) / (c + i d) == [(a + i b) * (c - i d)] / (c*c + d*d)</span>
<span class="comment">// == [(a*c + b*d) / (c*c + d*d)] + i [(b*c - a*d) / (c*c + d*d)]</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Div</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">div</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">let</span> <span class="ident">norm_sqr</span> <span class="op">=</span> <span class="ident">other</span>.<span class="ident">norm_sqr</span>();
<span class="kw">let</span> <span class="ident">re</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">re</span>.<span class="ident">clone</span>() <span class="op">*</span> <span class="ident">other</span>.<span class="ident">re</span>.<span class="ident">clone</span>() <span class="op">+</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">clone</span>() <span class="op">*</span> <span class="ident">other</span>.<span class="ident">im</span>.<span class="ident">clone</span>();
<span class="kw">let</span> <span class="ident">im</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">im</span> <span class="op">*</span> <span class="ident">other</span>.<span class="ident">re</span> <span class="op">-</span> <span class="self">self</span>.<span class="ident">re</span> <span class="op">*</span> <span class="ident">other</span>.<span class="ident">im</span>;
<span class="ident">Complex::new</span>(<span class="ident">re</span> <span class="op">/</span> <span class="ident">norm_sqr</span>.<span class="ident">clone</span>(), <span class="ident">im</span> <span class="op">/</span> <span class="ident">norm_sqr</span>)
}
}
<span class="macro">forward_all_binop!</span>(<span class="kw">impl</span> <span class="ident">Rem</span>, <span class="ident">rem</span>);
<span class="comment">// Attempts to identify the gaussian integer whose product with `modulus`</span>
<span class="comment">// is closest to `self`.</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Rem</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">rem</span>(<span class="self">self</span>, <span class="ident">modulus</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="kw">let</span> <span class="ident">Complex</span> { <span class="ident">re</span>, <span class="ident">im</span> } <span class="op">=</span> <span class="self">self</span>.<span class="ident">clone</span>() <span class="op">/</span> <span class="ident">modulus</span>.<span class="ident">clone</span>();
<span class="comment">// This is the gaussian integer corresponding to the true ratio</span>
<span class="comment">// rounded towards zero.</span>
<span class="kw">let</span> (<span class="ident">re0</span>, <span class="ident">im0</span>) <span class="op">=</span> (<span class="ident">re</span>.<span class="ident">clone</span>() <span class="op">-</span> <span class="ident">re</span> <span class="op">%</span> <span class="ident">T::one</span>(), <span class="ident">im</span>.<span class="ident">clone</span>() <span class="op">-</span> <span class="ident">im</span> <span class="op">%</span> <span class="ident">T::one</span>());
<span class="self">self</span> <span class="op">-</span> <span class="ident">modulus</span> <span class="op">*</span> <span class="ident">Complex::new</span>(<span class="ident">re0</span>, <span class="ident">im0</span>)
}
}
<span class="comment">// Op Assign</span>
<span class="kw">mod</span> <span class="ident">opassign</span> {
<span class="kw">use</span> <span class="ident">std::ops</span>::{<span class="ident">AddAssign</span>, <span class="ident">SubAssign</span>, <span class="ident">MulAssign</span>, <span class="ident">DivAssign</span>, <span class="ident">RemAssign</span>};
<span class="kw">use</span> <span class="ident">traits::NumAssign</span>;
<span class="kw">use</span> <span class="ident">Complex</span>;
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">AddAssign</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">add_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) {
<span class="self">self</span>.<span class="ident">re</span> <span class="op">+</span><span class="op">=</span> <span class="ident">other</span>.<span class="ident">re</span>;
<span class="self">self</span>.<span class="ident">im</span> <span class="op">+</span><span class="op">=</span> <span class="ident">other</span>.<span class="ident">im</span>;
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">SubAssign</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">sub_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) {
<span class="self">self</span>.<span class="ident">re</span> <span class="op">-</span><span class="op">=</span> <span class="ident">other</span>.<span class="ident">re</span>;
<span class="self">self</span>.<span class="ident">im</span> <span class="op">-</span><span class="op">=</span> <span class="ident">other</span>.<span class="ident">im</span>;
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">MulAssign</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">mul_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">clone</span>() <span class="op">*</span> <span class="ident">other</span>;
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">DivAssign</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">div_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">clone</span>() <span class="op">/</span> <span class="ident">other</span>;
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">RemAssign</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">rem_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">clone</span>() <span class="op">%</span> <span class="ident">other</span>;
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">AddAssign</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">add_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) {
<span class="self">self</span>.<span class="ident">re</span> <span class="op">+</span><span class="op">=</span> <span class="ident">other</span>;
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">SubAssign</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">sub_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) {
<span class="self">self</span>.<span class="ident">re</span> <span class="op">-</span><span class="op">=</span> <span class="ident">other</span>;
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">MulAssign</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">mul_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) {
<span class="self">self</span>.<span class="ident">re</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">other</span>.<span class="ident">clone</span>();
<span class="self">self</span>.<span class="ident">im</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">other</span>;
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">DivAssign</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">div_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) {
<span class="self">self</span>.<span class="ident">re</span> <span class="op">/</span><span class="op">=</span> <span class="ident">other</span>.<span class="ident">clone</span>();
<span class="self">self</span>.<span class="ident">im</span> <span class="op">/</span><span class="op">=</span> <span class="ident">other</span>;
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">RemAssign</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">rem_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">clone</span>() <span class="op">%</span> <span class="ident">other</span>;
}
}
<span class="macro">macro_rules!</span> <span class="ident">forward_op_assign</span> {
(<span class="kw">impl</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span>:<span class="ident">ident</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>:<span class="ident">ident</span>) <span class="op">=</span><span class="op">></span> {
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) {
<span class="self">self</span>.<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>.<span class="ident">clone</span>())
}
}
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">T</span>) {
<span class="self">self</span>.<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>.<span class="ident">clone</span>())
}
}
}
}
<span class="macro">forward_op_assign!</span>(<span class="kw">impl</span> <span class="ident">AddAssign</span>, <span class="ident">add_assign</span>);
<span class="macro">forward_op_assign!</span>(<span class="kw">impl</span> <span class="ident">SubAssign</span>, <span class="ident">sub_assign</span>);
<span class="macro">forward_op_assign!</span>(<span class="kw">impl</span> <span class="ident">MulAssign</span>, <span class="ident">mul_assign</span>);
<span class="macro">forward_op_assign!</span>(<span class="kw">impl</span> <span class="ident">DivAssign</span>, <span class="ident">div_assign</span>);
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">RemAssign</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">rem_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>) {
<span class="self">self</span>.<span class="ident">rem_assign</span>(<span class="ident">other</span>.<span class="ident">clone</span>())
}
}
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span> <span class="ident">RemAssign</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">rem_assign</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">T</span>) {
<span class="self">self</span>.<span class="ident">rem_assign</span>(<span class="ident">other</span>.<span class="ident">clone</span>())
}
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">Neg</span><span class="op"><</span><span class="ident">Output</span> <span class="op">=</span> <span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="ident">Neg</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">neg</span>(<span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="op">-</span><span class="self">self</span>.<span class="ident">re</span>, <span class="op">-</span><span class="self">self</span>.<span class="ident">im</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">Neg</span><span class="op"><</span><span class="ident">Output</span> <span class="op">=</span> <span class="ident">T</span><span class="op">></span><span class="op">></span> <span class="ident">Neg</span> <span class="kw">for</span> <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">neg</span>(<span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="op">-</span><span class="self">self</span>.<span class="ident">clone</span>()
}
}
<span class="macro">macro_rules!</span> <span class="ident">real_arithmetic</span> {
(@<span class="ident">forward</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span>:<span class="ident">ident</span>::<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>:<span class="ident">ident</span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span>:<span class="ident">ident</span>),<span class="kw-2">*</span>) <span class="op">=</span><span class="op">></span> (
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="self">self</span>.<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>.<span class="ident">clone</span>())
}
}
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="self">self</span>.<span class="ident">clone</span>().<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="lifetime">'b</span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="kw-2">&</span><span class="lifetime">'b</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="self">self</span>.<span class="ident">clone</span>().<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>.<span class="ident">clone</span>())
}
}
$(
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span> {
<span class="self">self</span>.<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>.<span class="ident">clone</span>())
}
}
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span> {
<span class="self">self</span>.<span class="ident">clone</span>().<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="lifetime">'b</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">imp</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="kw-2">&</span><span class="lifetime">'b</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span> {
<span class="self">self</span>.<span class="ident">clone</span>().<span class="macro-nonterminal">$</span><span class="macro-nonterminal">method</span>(<span class="ident">other</span>.<span class="ident">clone</span>())
}
}
)<span class="op">*</span>
);
($(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span>:<span class="ident">ident</span>),<span class="kw-2">*</span>) <span class="op">=</span><span class="op">></span> (
<span class="macro">real_arithmetic!</span>(@<span class="ident">forward</span> <span class="ident">Add::add</span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span>),<span class="kw-2">*</span>);
<span class="macro">real_arithmetic!</span>(@<span class="ident">forward</span> <span class="ident">Sub::sub</span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span>),<span class="kw-2">*</span>);
<span class="macro">real_arithmetic!</span>(@<span class="ident">forward</span> <span class="ident">Mul::mul</span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span>),<span class="kw-2">*</span>);
<span class="macro">real_arithmetic!</span>(@<span class="ident">forward</span> <span class="ident">Div::div</span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span>),<span class="kw-2">*</span>);
<span class="macro">real_arithmetic!</span>(@<span class="ident">forward</span> <span class="ident">Rem::rem</span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span>),<span class="kw-2">*</span>);
$(
<span class="kw">impl</span> <span class="ident">Add</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">add</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span> <span class="op">+</span> <span class="ident">other</span>.<span class="ident">re</span>, <span class="ident">other</span>.<span class="ident">im</span>)
}
}
<span class="kw">impl</span> <span class="ident">Sub</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">sub</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span> <span class="op">-</span> <span class="ident">other</span>.<span class="ident">re</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">real::zero</span>() <span class="op">-</span> <span class="ident">other</span>.<span class="ident">im</span>)
}
}
<span class="kw">impl</span> <span class="ident">Mul</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">mul</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span> <span class="op">*</span> <span class="ident">other</span>.<span class="ident">re</span>, <span class="self">self</span> <span class="op">*</span> <span class="ident">other</span>.<span class="ident">im</span>)
}
}
<span class="kw">impl</span> <span class="ident">Div</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">div</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span> {
<span class="comment">// a / (c + i d) == [a * (c - i d)] / (c*c + d*d)</span>
<span class="kw">let</span> <span class="ident">norm_sqr</span> <span class="op">=</span> <span class="ident">other</span>.<span class="ident">norm_sqr</span>();
<span class="ident">Complex::new</span>(<span class="self">self</span> <span class="op">*</span> <span class="ident">other</span>.<span class="ident">re</span> <span class="op">/</span> <span class="ident">norm_sqr</span>.<span class="ident">clone</span>(),
<span class="macro-nonterminal">$</span><span class="macro-nonterminal">real::zero</span>() <span class="op">-</span> <span class="self">self</span> <span class="op">*</span> <span class="ident">other</span>.<span class="ident">im</span> <span class="op">/</span> <span class="ident">norm_sqr</span>)
}
}
<span class="kw">impl</span> <span class="ident">Rem</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">rem</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">real</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span>, <span class="self">Self</span><span class="ident">::zero</span>()) <span class="op">%</span> <span class="ident">other</span>
}
}
)<span class="op">*</span>
);
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Add</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">add</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span> <span class="op">+</span> <span class="ident">other</span>, <span class="self">self</span>.<span class="ident">im</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Sub</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">sub</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span> <span class="op">-</span> <span class="ident">other</span>, <span class="self">self</span>.<span class="ident">im</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Mul</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">mul</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span> <span class="op">*</span> <span class="ident">other</span>.<span class="ident">clone</span>(), <span class="self">self</span>.<span class="ident">im</span> <span class="op">*</span> <span class="ident">other</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Div</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">div</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="self">self</span>.<span class="ident">re</span> <span class="op">/</span> <span class="ident">other</span>.<span class="ident">clone</span>(), <span class="self">self</span>.<span class="ident">im</span> <span class="op">/</span> <span class="ident">other</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Rem</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Output</span> <span class="op">=</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">rem</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="self">self</span> <span class="op">%</span> <span class="ident">Complex::new</span>(<span class="ident">other</span>, <span class="ident">T::zero</span>())
}
}
<span class="macro">real_arithmetic!</span>(<span class="ident">usize</span>, <span class="ident">u8</span>, <span class="ident">u16</span>, <span class="ident">u32</span>, <span class="ident">u64</span>, <span class="ident">isize</span>, <span class="ident">i8</span>, <span class="ident">i16</span>, <span class="ident">i32</span>, <span class="ident">i64</span>, <span class="ident">f32</span>, <span class="ident">f64</span>);
<span class="comment">/* constants */</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">Zero</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">zero</span>() <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="ident">Zero::zero</span>(), <span class="ident">Zero::zero</span>())
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_zero</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="self">self</span>.<span class="ident">re</span>.<span class="ident">is_zero</span>() <span class="op">&&</span> <span class="self">self</span>.<span class="ident">im</span>.<span class="ident">is_zero</span>()
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span><span class="op">></span> <span class="ident">One</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">one</span>() <span class="op">-</span><span class="op">></span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">Complex::new</span>(<span class="ident">One::one</span>(), <span class="ident">Zero::zero</span>())
}
}
<span class="macro">macro_rules!</span> <span class="ident">write_complex</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">f</span>:<span class="ident">ident</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">prefix</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">re</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">im</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>:<span class="ident">ident</span>) <span class="op">=</span><span class="op">></span> {{
<span class="kw">let</span> <span class="ident">abs_re</span> <span class="op">=</span> <span class="kw">if</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">re</span> <span class="op"><</span> <span class="ident">Zero::zero</span>() { <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T::zero</span>() <span class="op">-</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">re</span>.<span class="ident">clone</span>() } <span class="kw">else</span> { <span class="macro-nonterminal">$</span><span class="macro-nonterminal">re</span>.<span class="ident">clone</span>() };
<span class="kw">let</span> <span class="ident">abs_im</span> <span class="op">=</span> <span class="kw">if</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">im</span> <span class="op"><</span> <span class="ident">Zero::zero</span>() { <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T::zero</span>() <span class="op">-</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">im</span>.<span class="ident">clone</span>() } <span class="kw">else</span> { <span class="macro-nonterminal">$</span><span class="macro-nonterminal">im</span>.<span class="ident">clone</span>() };
<span class="kw">let</span> <span class="ident">real</span>: <span class="ident">String</span>;
<span class="kw">let</span> <span class="ident">imag</span>: <span class="ident">String</span>;
<span class="kw">if</span> <span class="kw">let</span> <span class="prelude-val">Some</span>(<span class="ident">prec</span>) <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">f</span>.<span class="ident">precision</span>() {
<span class="ident">real</span> <span class="op">=</span> <span class="macro">format!</span>(<span class="macro">concat!</span>(<span class="string">"{:.1$"</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>, <span class="string">"}"</span>), <span class="ident">abs_re</span>, <span class="ident">prec</span>);
<span class="ident">imag</span> <span class="op">=</span> <span class="macro">format!</span>(<span class="macro">concat!</span>(<span class="string">"{:.1$"</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>, <span class="string">"}"</span>), <span class="ident">abs_im</span>, <span class="ident">prec</span>);
}
<span class="kw">else</span> {
<span class="ident">real</span> <span class="op">=</span> <span class="macro">format!</span>(<span class="macro">concat!</span>(<span class="string">"{:"</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>, <span class="string">"}"</span>), <span class="ident">abs_re</span>);
<span class="ident">imag</span> <span class="op">=</span> <span class="macro">format!</span>(<span class="macro">concat!</span>(<span class="string">"{:"</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>, <span class="string">"}"</span>), <span class="ident">abs_im</span>);
}
<span class="kw">let</span> <span class="ident">prefix</span> <span class="op">=</span> <span class="kw">if</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">f</span>.<span class="ident">alternate</span>() { <span class="macro-nonterminal">$</span><span class="macro-nonterminal">prefix</span> } <span class="kw">else</span> { <span class="string">""</span> };
<span class="kw">let</span> <span class="ident">sign</span> <span class="op">=</span> <span class="kw">if</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">re</span> <span class="op"><</span> <span class="ident">Zero::zero</span>() {
<span class="string">"-"</span>
} <span class="kw">else</span> <span class="kw">if</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">f</span>.<span class="ident">sign_plus</span>() {
<span class="string">"+"</span>
} <span class="kw">else</span> {
<span class="string">""</span>
};
<span class="kw">let</span> <span class="ident">complex</span> <span class="op">=</span> <span class="kw">if</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">im</span> <span class="op"><</span> <span class="ident">Zero::zero</span>() {
<span class="macro">format!</span>(<span class="string">"{}{pre}{re}-{pre}{im}i"</span>, <span class="ident">sign</span>, <span class="ident">re</span><span class="op">=</span><span class="ident">real</span>, <span class="ident">im</span><span class="op">=</span><span class="ident">imag</span>, <span class="ident">pre</span><span class="op">=</span><span class="ident">prefix</span>)
}
<span class="kw">else</span> {
<span class="macro">format!</span>(<span class="string">"{}{pre}{re}+{pre}{im}i"</span>, <span class="ident">sign</span>, <span class="ident">re</span><span class="op">=</span><span class="ident">real</span>, <span class="ident">im</span><span class="op">=</span><span class="ident">imag</span>, <span class="ident">pre</span><span class="op">=</span><span class="ident">prefix</span>)
};
<span class="kw">if</span> <span class="kw">let</span> <span class="prelude-val">Some</span>(<span class="ident">width</span>) <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">f</span>.<span class="ident">width</span>() {
<span class="macro">write!</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">f</span>, <span class="string">"{0: >1$}"</span>, <span class="ident">complex</span>, <span class="ident">width</span>)
}
<span class="kw">else</span> {
<span class="macro">write!</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">f</span>, <span class="string">"{}"</span>, <span class="ident">complex</span>)
}
}}
}
<span class="comment">/* string conversions */</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">fmt::Display</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">fmt::Display</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">PartialOrd</span> <span class="op">+</span> <span class="ident">Clone</span>
{
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt::Formatter</span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt::Result</span> {
<span class="macro">write_complex!</span>(<span class="ident">f</span>, <span class="string">""</span>, <span class="string">""</span>, <span class="self">self</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span>, <span class="ident">T</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">fmt::LowerExp</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">fmt::LowerExp</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">PartialOrd</span> <span class="op">+</span> <span class="ident">Clone</span>
{
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt::Formatter</span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt::Result</span> {
<span class="macro">write_complex!</span>(<span class="ident">f</span>, <span class="string">"e"</span>, <span class="string">""</span>, <span class="self">self</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span>, <span class="ident">T</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">fmt::UpperExp</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">fmt::UpperExp</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">PartialOrd</span> <span class="op">+</span> <span class="ident">Clone</span>
{
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt::Formatter</span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt::Result</span> {
<span class="macro">write_complex!</span>(<span class="ident">f</span>, <span class="string">"E"</span>, <span class="string">""</span>, <span class="self">self</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span>, <span class="ident">T</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">fmt::LowerHex</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">fmt::LowerHex</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">PartialOrd</span> <span class="op">+</span> <span class="ident">Clone</span>
{
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt::Formatter</span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt::Result</span> {
<span class="macro">write_complex!</span>(<span class="ident">f</span>, <span class="string">"x"</span>, <span class="string">"0x"</span>, <span class="self">self</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span>, <span class="ident">T</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">fmt::UpperHex</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">fmt::UpperHex</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">PartialOrd</span> <span class="op">+</span> <span class="ident">Clone</span>
{
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt::Formatter</span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt::Result</span> {
<span class="macro">write_complex!</span>(<span class="ident">f</span>, <span class="string">"X"</span>, <span class="string">"0x"</span>, <span class="self">self</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span>, <span class="ident">T</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">fmt::Octal</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">fmt::Octal</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">PartialOrd</span> <span class="op">+</span> <span class="ident">Clone</span>
{
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt::Formatter</span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt::Result</span> {
<span class="macro">write_complex!</span>(<span class="ident">f</span>, <span class="string">"o"</span>, <span class="string">"0o"</span>, <span class="self">self</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span>, <span class="ident">T</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">fmt::Binary</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">fmt::Binary</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">PartialOrd</span> <span class="op">+</span> <span class="ident">Clone</span>
{
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt::Formatter</span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt::Result</span> {
<span class="macro">write_complex!</span>(<span class="ident">f</span>, <span class="string">"b"</span>, <span class="string">"0b"</span>, <span class="self">self</span>.<span class="ident">re</span>, <span class="self">self</span>.<span class="ident">im</span>, <span class="ident">T</span>)
}
}
<span class="kw">fn</span> <span class="ident">from_str_generic</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">E</span>, <span class="ident">F</span><span class="op">></span>(<span class="ident">s</span>: <span class="kw-2">&</span><span class="ident">str</span>, <span class="ident">from</span>: <span class="ident">F</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>, <span class="ident">ParseComplexError</span><span class="op"><</span><span class="ident">E</span><span class="op">></span><span class="op">></span>
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">Fn</span>(<span class="kw-2">&</span><span class="ident">str</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">E</span><span class="op">></span>, <span class="ident">T</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Num</span>
{
<span class="kw">let</span> <span class="ident">imag</span> <span class="op">=</span> <span class="kw">match</span> <span class="ident">s</span>.<span class="ident">rfind</span>(<span class="string">'j'</span>) {
<span class="prelude-val">None</span> <span class="op">=</span><span class="op">></span> <span class="string">'i'</span>,
<span class="kw">_</span> <span class="op">=</span><span class="op">></span> <span class="string">'j'</span>
};
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">b</span> <span class="op">=</span> <span class="ident">String::with_capacity</span>(<span class="ident">s</span>.<span class="ident">len</span>());
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">first</span> <span class="op">=</span> <span class="bool-val">true</span>;
<span class="kw">let</span> <span class="ident">char_indices</span> <span class="op">=</span> <span class="ident">s</span>.<span class="ident">char_indices</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">pc</span> <span class="op">=</span> <span class="string">' '</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">split_index</span> <span class="op">=</span> <span class="ident">s</span>.<span class="ident">len</span>();
<span class="kw">for</span> (<span class="ident">i</span>, <span class="ident">cc</span>) <span class="kw">in</span> <span class="ident">char_indices</span> {
<span class="kw">if</span> <span class="ident">cc</span> <span class="op">=</span><span class="op">=</span> <span class="string">'+'</span> <span class="op">&&</span> <span class="ident">pc</span> <span class="op">!</span><span class="op">=</span> <span class="string">'e'</span> <span class="op">&&</span> <span class="ident">pc</span> <span class="op">!</span><span class="op">=</span> <span class="string">'E'</span> <span class="op">&&</span> <span class="ident">i</span> <span class="op">></span> <span class="number">0</span> {
<span class="comment">// ignore '+' if part of an exponent</span>
<span class="kw">if</span> <span class="ident">first</span> {
<span class="ident">split_index</span> <span class="op">=</span> <span class="ident">i</span>;
<span class="ident">first</span> <span class="op">=</span> <span class="bool-val">false</span>;
}
<span class="comment">// don't carry '+' over into b</span>
<span class="ident">pc</span> <span class="op">=</span> <span class="string">' '</span>;
<span class="kw">continue</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">cc</span> <span class="op">=</span><span class="op">=</span> <span class="string">'-'</span> <span class="op">&&</span> <span class="ident">pc</span> <span class="op">!</span><span class="op">=</span> <span class="string">'e'</span> <span class="op">&&</span> <span class="ident">pc</span> <span class="op">!</span><span class="op">=</span> <span class="string">'E'</span> <span class="op">&&</span> <span class="ident">i</span> <span class="op">></span> <span class="number">0</span> {
<span class="comment">// ignore '-' if part of an exponent or begins the string</span>
<span class="kw">if</span> <span class="ident">first</span> {
<span class="ident">split_index</span> <span class="op">=</span> <span class="ident">i</span>;
<span class="ident">first</span> <span class="op">=</span> <span class="bool-val">false</span>;
}
<span class="comment">// DO carry '-' over into b</span>
}
<span class="kw">if</span> <span class="ident">pc</span> <span class="op">=</span><span class="op">=</span> <span class="string">'-'</span> <span class="op">&&</span> <span class="ident">cc</span> <span class="op">=</span><span class="op">=</span> <span class="string">' '</span> <span class="op">&&</span> <span class="op">!</span><span class="ident">first</span> {
<span class="comment">// ignore whitespace between minus sign and next number</span>
<span class="kw">continue</span>;
}
<span class="kw">if</span> <span class="op">!</span><span class="ident">first</span> {
<span class="ident">b</span>.<span class="ident">push</span>(<span class="ident">cc</span>);
}
<span class="ident">pc</span> <span class="op">=</span> <span class="ident">cc</span>;
}
<span class="comment">// split off real and imaginary parts, trim whitespace</span>
<span class="kw">let</span> (<span class="ident">a</span>, <span class="kw">_</span>) <span class="op">=</span> <span class="ident">s</span>.<span class="ident">split_at</span>(<span class="ident">split_index</span>);
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">a</span>.<span class="ident">trim_right</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">b</span> <span class="op">=</span> <span class="ident">b</span>.<span class="ident">trim_left</span>();
<span class="comment">// input was either pure real or pure imaginary</span>
<span class="kw">if</span> <span class="ident">b</span>.<span class="ident">is_empty</span>() {
<span class="ident">b</span> <span class="op">=</span> <span class="kw">match</span> <span class="ident">a</span>.<span class="ident">ends_with</span>(<span class="ident">imag</span>) {
<span class="bool-val">false</span> <span class="op">=</span><span class="op">></span> <span class="string">"0i"</span>,
<span class="bool-val">true</span> <span class="op">=</span><span class="op">></span> <span class="string">"0"</span>
};
}
<span class="kw">let</span> <span class="ident">re</span>;
<span class="kw">let</span> <span class="ident">im</span>;
<span class="kw">if</span> <span class="ident">a</span>.<span class="ident">ends_with</span>(<span class="ident">imag</span>) {
<span class="ident">im</span> <span class="op">=</span> <span class="ident">a</span>; <span class="ident">re</span> <span class="op">=</span> <span class="ident">b</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">b</span>.<span class="ident">ends_with</span>(<span class="ident">imag</span>) {
<span class="ident">re</span> <span class="op">=</span> <span class="ident">a</span>; <span class="ident">im</span> <span class="op">=</span> <span class="ident">b</span>;
} <span class="kw">else</span> {
<span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">ParseComplexError::new</span>());
}
<span class="comment">// parse re</span>
<span class="kw">let</span> <span class="ident">re</span> <span class="op">=</span> <span class="macro">try!</span>(<span class="ident">from</span>(<span class="ident">re</span>).<span class="ident">map_err</span>(<span class="ident">ParseComplexError::from_error</span>));
<span class="comment">// pop imaginary unit off</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">im</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">im</span>[..<span class="ident">im</span>.<span class="ident">len</span>()<span class="op">-</span><span class="number">1</span>];
<span class="comment">// handle im == "i" or im == "-i"</span>
<span class="kw">if</span> <span class="ident">im</span>.<span class="ident">is_empty</span>() <span class="op">|</span><span class="op">|</span> <span class="ident">im</span> <span class="op">=</span><span class="op">=</span> <span class="string">"+"</span> {
<span class="ident">im</span> <span class="op">=</span> <span class="string">"1"</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">im</span> <span class="op">=</span><span class="op">=</span> <span class="string">"-"</span> {
<span class="ident">im</span> <span class="op">=</span> <span class="string">"-1"</span>;
}
<span class="comment">// parse im</span>
<span class="kw">let</span> <span class="ident">im</span> <span class="op">=</span> <span class="macro">try!</span>(<span class="ident">from</span>(<span class="ident">im</span>).<span class="ident">map_err</span>(<span class="ident">ParseComplexError::from_error</span>));
<span class="prelude-val">Ok</span>(<span class="ident">Complex::new</span>(<span class="ident">re</span>, <span class="ident">im</span>))
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">FromStr</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">FromStr</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">Clone</span>
{
<span class="kw">type</span> <span class="prelude-val">Err</span> <span class="op">=</span> <span class="ident">ParseComplexError</span><span class="op"><</span><span class="ident">T::Err</span><span class="op">></span>;
<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> <span class="ident">from_str</span>(<span class="ident">s</span>: <span class="kw-2">&</span><span class="ident">str</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Result</span><span class="op"><</span><span class="self">Self</span>, <span class="self">Self</span><span class="ident">::Err</span><span class="op">></span>
{
<span class="ident">from_str_generic</span>(<span class="ident">s</span>, <span class="ident">T::from_str</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Num</span> <span class="op">+</span> <span class="ident">Clone</span><span class="op">></span> <span class="ident">Num</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">FromStrRadixErr</span> <span class="op">=</span> <span class="ident">ParseComplexError</span><span class="op"><</span><span class="ident">T::FromStrRadixErr</span><span class="op">></span>;
<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> <span class="ident">from_str_radix</span>(<span class="ident">s</span>: <span class="kw-2">&</span><span class="ident">str</span>, <span class="ident">radix</span>: <span class="ident">u32</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Result</span><span class="op"><</span><span class="self">Self</span>, <span class="self">Self</span><span class="ident">::FromStrRadixErr</span><span class="op">></span>
{
<span class="ident">from_str_generic</span>(<span class="ident">s</span>, <span class="op">|</span><span class="ident">x</span><span class="op">|</span> <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">T</span>, <span class="ident">T::FromStrRadixErr</span><span class="op">></span> {
<span class="ident">T::from_str_radix</span>(<span class="ident">x</span>, <span class="ident">radix</span>) })
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"serde"</span>)]</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">serde::Serialize</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>
<span class="kw">where</span> <span class="ident">T</span>: <span class="ident">serde::Serialize</span>
{
<span class="kw">fn</span> <span class="ident">serialize</span><span class="op"><</span><span class="ident">S</span><span class="op">></span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">serializer</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">S</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Result</span><span class="op"><</span>(), <span class="ident">S::Error</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">S</span>: <span class="ident">serde::Serializer</span>
{
(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">re</span>, <span class="kw-2">&</span><span class="self">self</span>.<span class="ident">im</span>).<span class="ident">serialize</span>(<span class="ident">serializer</span>)
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"serde"</span>)]</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">serde::Deserialize</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">serde::Deserialize</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">Clone</span>
{
<span class="kw">fn</span> <span class="ident">deserialize</span><span class="op"><</span><span class="ident">D</span><span class="op">></span>(<span class="ident">deserializer</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">D</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Result</span><span class="op"><</span><span class="self">Self</span>, <span class="ident">D::Error</span><span class="op">></span> <span class="kw">where</span>
<span class="ident">D</span>: <span class="ident">serde::Deserializer</span>,
{
<span class="kw">let</span> (<span class="ident">re</span>, <span class="ident">im</span>) <span class="op">=</span> <span class="macro">try!</span>(<span class="ident">serde::Deserialize::deserialize</span>(<span class="ident">deserializer</span>));
<span class="prelude-val">Ok</span>(<span class="ident">Complex::new</span>(<span class="ident">re</span>, <span class="ident">im</span>))
}
}
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Debug</span>, <span class="ident">PartialEq</span>)]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">ParseComplexError</span><span class="op"><</span><span class="ident">E</span><span class="op">></span>
{
<span class="ident">kind</span>: <span class="ident">ComplexErrorKind</span><span class="op"><</span><span class="ident">E</span><span class="op">></span>,
}
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Debug</span>, <span class="ident">PartialEq</span>)]</span>
<span class="kw">enum</span> <span class="ident">ComplexErrorKind</span><span class="op"><</span><span class="ident">E</span><span class="op">></span>
{
<span class="ident">ParseError</span>(<span class="ident">E</span>),
<span class="ident">ExprError</span>
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">E</span><span class="op">></span> <span class="ident">ParseComplexError</span><span class="op"><</span><span class="ident">E</span><span class="op">></span>
{
<span class="kw">fn</span> <span class="ident">new</span>() <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="ident">ParseComplexError</span> {
<span class="ident">kind</span>: <span class="ident">ComplexErrorKind::ExprError</span>,
}
}
<span class="kw">fn</span> <span class="ident">from_error</span>(<span class="ident">error</span>: <span class="ident">E</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="ident">ParseComplexError</span> {
<span class="ident">kind</span>: <span class="ident">ComplexErrorKind::ParseError</span>(<span class="ident">error</span>),
}
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">E</span>: <span class="ident">Error</span><span class="op">></span> <span class="ident">Error</span> <span class="kw">for</span> <span class="ident">ParseComplexError</span><span class="op"><</span><span class="ident">E</span><span class="op">></span>
{
<span class="kw">fn</span> <span class="ident">description</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="kw-2">&</span><span class="ident">str</span> {
<span class="kw">match</span> <span class="self">self</span>.<span class="ident">kind</span> {
<span class="ident">ComplexErrorKind::ParseError</span>(<span class="kw-2">ref</span> <span class="ident">e</span>) <span class="op">=</span><span class="op">></span> <span class="ident">e</span>.<span class="ident">description</span>(),
<span class="ident">ComplexErrorKind::ExprError</span> <span class="op">=</span><span class="op">></span> <span class="string">"invalid or unsupported complex expression"</span>
}
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">E</span>: <span class="ident">Error</span><span class="op">></span> <span class="ident">fmt::Display</span> <span class="kw">for</span> <span class="ident">ParseComplexError</span><span class="op"><</span><span class="ident">E</span><span class="op">></span>
{
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt::Formatter</span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt::Result</span> {
<span class="self">self</span>.<span class="ident">description</span>().<span class="ident">fmt</span>(<span class="ident">f</span>)
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">fn</span> <span class="ident">hash</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">hash::Hash</span><span class="op">></span>(<span class="ident">x</span>: <span class="kw-2">&</span><span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">u64</span> {
<span class="kw">use</span> <span class="ident">std::hash</span>::{<span class="ident">BuildHasher</span>, <span class="ident">Hasher</span>};
<span class="kw">use</span> <span class="ident">std::collections::hash_map::RandomState</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">hasher</span> <span class="op">=</span> <span class="op"><</span><span class="ident">RandomState</span> <span class="kw">as</span> <span class="ident">BuildHasher</span><span class="op">></span><span class="ident">::Hasher::new</span>();
<span class="ident">x</span>.<span class="ident">hash</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">hasher</span>);
<span class="ident">hasher</span>.<span class="ident">finish</span>()
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">mod</span> <span class="ident">test</span> {
<span class="attribute">#![<span class="ident">allow</span>(<span class="ident">non_upper_case_globals</span>)]</span>
<span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">Complex64</span>, <span class="ident">Complex</span>};
<span class="kw">use</span> <span class="ident">std::f64</span>;
<span class="kw">use</span> <span class="ident">std::str::FromStr</span>;
<span class="kw">use</span> <span class="ident">traits</span>::{<span class="ident">Zero</span>, <span class="ident">One</span>, <span class="ident">Float</span>, <span class="ident">Num</span>};
<span class="kw">pub</span> <span class="kw">const</span> <span class="ident">_0_0i</span> : <span class="ident">Complex64</span> <span class="op">=</span> <span class="ident">Complex</span> { <span class="ident">re</span>: <span class="number">0.0</span>, <span class="ident">im</span>: <span class="number">0.0</span> };
<span class="kw">pub</span> <span class="kw">const</span> <span class="ident">_1_0i</span> : <span class="ident">Complex64</span> <span class="op">=</span> <span class="ident">Complex</span> { <span class="ident">re</span>: <span class="number">1.0</span>, <span class="ident">im</span>: <span class="number">0.0</span> };
<span class="kw">pub</span> <span class="kw">const</span> <span class="ident">_1_1i</span> : <span class="ident">Complex64</span> <span class="op">=</span> <span class="ident">Complex</span> { <span class="ident">re</span>: <span class="number">1.0</span>, <span class="ident">im</span>: <span class="number">1.0</span> };
<span class="kw">pub</span> <span class="kw">const</span> <span class="ident">_0_1i</span> : <span class="ident">Complex64</span> <span class="op">=</span> <span class="ident">Complex</span> { <span class="ident">re</span>: <span class="number">0.0</span>, <span class="ident">im</span>: <span class="number">1.0</span> };
<span class="kw">pub</span> <span class="kw">const</span> <span class="ident">_neg1_1i</span> : <span class="ident">Complex64</span> <span class="op">=</span> <span class="ident">Complex</span> { <span class="ident">re</span>: <span class="op">-</span><span class="number">1.0</span>, <span class="ident">im</span>: <span class="number">1.0</span> };
<span class="kw">pub</span> <span class="kw">const</span> <span class="ident">_05_05i</span> : <span class="ident">Complex64</span> <span class="op">=</span> <span class="ident">Complex</span> { <span class="ident">re</span>: <span class="number">0.5</span>, <span class="ident">im</span>: <span class="number">0.5</span> };
<span class="kw">pub</span> <span class="kw">const</span> <span class="ident">all_consts</span> : [<span class="ident">Complex64</span>; <span class="number">5</span>] <span class="op">=</span> [<span class="ident">_0_0i</span>, <span class="ident">_1_0i</span>, <span class="ident">_1_1i</span>, <span class="ident">_neg1_1i</span>, <span class="ident">_05_05i</span>];
<span class="kw">pub</span> <span class="kw">const</span> <span class="ident">_4_2i</span> : <span class="ident">Complex64</span> <span class="op">=</span> <span class="ident">Complex</span> { <span class="ident">re</span>: <span class="number">4.0</span>, <span class="ident">im</span>: <span class="number">2.0</span> };
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_consts</span>() {
<span class="comment">// check our constants are what Complex::new creates</span>
<span class="kw">fn</span> <span class="ident">test</span>(<span class="ident">c</span> : <span class="ident">Complex64</span>, <span class="ident">r</span> : <span class="ident">f64</span>, <span class="ident">i</span>: <span class="ident">f64</span>) {
<span class="macro">assert_eq!</span>(<span class="ident">c</span>, <span class="ident">Complex::new</span>(<span class="ident">r</span>,<span class="ident">i</span>));
}
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="number">0.0</span>, <span class="number">0.0</span>);
<span class="ident">test</span>(<span class="ident">_1_0i</span>, <span class="number">1.0</span>, <span class="number">0.0</span>);
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="number">1.0</span>, <span class="number">1.0</span>);
<span class="ident">test</span>(<span class="ident">_neg1_1i</span>, <span class="op">-</span><span class="number">1.0</span>, <span class="number">1.0</span>);
<span class="ident">test</span>(<span class="ident">_05_05i</span>, <span class="number">0.5</span>, <span class="number">0.5</span>);
<span class="macro">assert_eq!</span>(<span class="ident">_0_0i</span>, <span class="ident">Zero::zero</span>());
<span class="macro">assert_eq!</span>(<span class="ident">_1_0i</span>, <span class="ident">One::one</span>());
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">target_arch</span> <span class="op">=</span> <span class="string">"x86"</span>, <span class="ident">ignore</span>)]</span>
<span class="comment">// FIXME #7158: (maybe?) currently failing on x86.</span>
<span class="kw">fn</span> <span class="ident">test_norm</span>() {
<span class="kw">fn</span> <span class="ident">test</span>(<span class="ident">c</span>: <span class="ident">Complex64</span>, <span class="ident">ns</span>: <span class="ident">f64</span>) {
<span class="macro">assert_eq!</span>(<span class="ident">c</span>.<span class="ident">norm_sqr</span>(), <span class="ident">ns</span>);
<span class="macro">assert_eq!</span>(<span class="ident">c</span>.<span class="ident">norm</span>(), <span class="ident">ns</span>.<span class="ident">sqrt</span>())
}
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="number">0.0</span>);
<span class="ident">test</span>(<span class="ident">_1_0i</span>, <span class="number">1.0</span>);
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="number">2.0</span>);
<span class="ident">test</span>(<span class="ident">_neg1_1i</span>, <span class="number">2.0</span>);
<span class="ident">test</span>(<span class="ident">_05_05i</span>, <span class="number">0.5</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_scale_unscale</span>() {
<span class="macro">assert_eq!</span>(<span class="ident">_05_05i</span>.<span class="ident">scale</span>(<span class="number">2.0</span>), <span class="ident">_1_1i</span>);
<span class="macro">assert_eq!</span>(<span class="ident">_1_1i</span>.<span class="ident">unscale</span>(<span class="number">2.0</span>), <span class="ident">_05_05i</span>);
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="macro">assert_eq!</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="number">2.0</span>).<span class="ident">unscale</span>(<span class="number">2.0</span>), <span class="ident">c</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_conj</span>() {
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="macro">assert_eq!</span>(<span class="ident">c</span>.<span class="ident">conj</span>(), <span class="ident">Complex::new</span>(<span class="ident">c</span>.<span class="ident">re</span>, <span class="op">-</span><span class="ident">c</span>.<span class="ident">im</span>));
<span class="macro">assert_eq!</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">conj</span>(), <span class="ident">c</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_inv</span>() {
<span class="macro">assert_eq!</span>(<span class="ident">_1_1i</span>.<span class="ident">inv</span>(), <span class="ident">_05_05i</span>.<span class="ident">conj</span>());
<span class="macro">assert_eq!</span>(<span class="ident">_1_0i</span>.<span class="ident">inv</span>(), <span class="ident">_1_0i</span>.<span class="ident">inv</span>());
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">should_panic</span>]</span>
<span class="kw">fn</span> <span class="ident">test_divide_by_zero_natural</span>() {
<span class="kw">let</span> <span class="ident">n</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">2</span>, <span class="number">3</span>);
<span class="kw">let</span> <span class="ident">d</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">0</span>, <span class="number">0</span>);
<span class="kw">let</span> <span class="ident">_x</span> <span class="op">=</span> <span class="ident">n</span> <span class="op">/</span> <span class="ident">d</span>;
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_inv_zero</span>() {
<span class="comment">// FIXME #20: should this really fail, or just NaN?</span>
<span class="macro">assert!</span>(<span class="ident">_0_0i</span>.<span class="ident">inv</span>().<span class="ident">is_nan</span>());
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_arg</span>() {
<span class="kw">fn</span> <span class="ident">test</span>(<span class="ident">c</span>: <span class="ident">Complex64</span>, <span class="ident">arg</span>: <span class="ident">f64</span>) {
<span class="macro">assert!</span>((<span class="ident">c</span>.<span class="ident">arg</span>() <span class="op">-</span> <span class="ident">arg</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="number">1.0e-6</span>)
}
<span class="ident">test</span>(<span class="ident">_1_0i</span>, <span class="number">0.0</span>);
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="number">0.25</span> <span class="op">*</span> <span class="ident">f64::consts::PI</span>);
<span class="ident">test</span>(<span class="ident">_neg1_1i</span>, <span class="number">0.75</span> <span class="op">*</span> <span class="ident">f64::consts::PI</span>);
<span class="ident">test</span>(<span class="ident">_05_05i</span>, <span class="number">0.25</span> <span class="op">*</span> <span class="ident">f64::consts::PI</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_polar_conv</span>() {
<span class="kw">fn</span> <span class="ident">test</span>(<span class="ident">c</span>: <span class="ident">Complex64</span>) {
<span class="kw">let</span> (<span class="ident">r</span>, <span class="ident">theta</span>) <span class="op">=</span> <span class="ident">c</span>.<span class="ident">to_polar</span>();
<span class="macro">assert!</span>((<span class="ident">c</span> <span class="op">-</span> <span class="ident">Complex::from_polar</span>(<span class="kw-2">&</span><span class="ident">r</span>, <span class="kw-2">&</span><span class="ident">theta</span>)).<span class="ident">norm</span>() <span class="op"><</span> <span class="number">1e-6</span>);
}
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() { <span class="ident">test</span>(<span class="ident">c</span>); }
}
<span class="kw">fn</span> <span class="ident">close</span>(<span class="ident">a</span>: <span class="ident">Complex64</span>, <span class="ident">b</span>: <span class="ident">Complex64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="ident">close_to_tol</span>(<span class="ident">a</span>, <span class="ident">b</span>, <span class="number">1e-10</span>)
}
<span class="kw">fn</span> <span class="ident">close_to_tol</span>(<span class="ident">a</span>: <span class="ident">Complex64</span>, <span class="ident">b</span>: <span class="ident">Complex64</span>, <span class="ident">tol</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="comment">// returns true if a and b are reasonably close</span>
(<span class="ident">a</span> <span class="op">=</span><span class="op">=</span> <span class="ident">b</span>) <span class="op">|</span><span class="op">|</span> (<span class="ident">a</span><span class="op">-</span><span class="ident">b</span>).<span class="ident">norm</span>() <span class="op"><</span> <span class="ident">tol</span>
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_exp</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">exp</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::E</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">exp</span>(), <span class="ident">_1_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">exp</span>(), <span class="ident">Complex::new</span>(<span class="number">1.0</span>.<span class="ident">cos</span>(), <span class="number">1.0</span>.<span class="ident">sin</span>())));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_05_05i</span>.<span class="ident">exp</span>()<span class="kw-2">*</span><span class="ident">_05_05i</span>.<span class="ident">exp</span>(), <span class="ident">_1_1i</span>.<span class="ident">exp</span>()));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="ident">f64::consts::PI</span>).<span class="ident">exp</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>)));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// e^conj(z) = conj(e^z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">exp</span>(), <span class="ident">c</span>.<span class="ident">exp</span>().<span class="ident">conj</span>()));
<span class="comment">// e^(z + 2 pi i) = e^z</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">exp</span>(), (<span class="ident">c</span> <span class="op">+</span> <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="kw-2">*</span><span class="number">2.0</span>)).<span class="ident">exp</span>()));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_ln</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">ln</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">ln</span>(), <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">ln</span>(), <span class="ident">Complex::new</span>(<span class="ident">f64::neg_infinity</span>(), <span class="number">0.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>((<span class="ident">_neg1_1i</span> <span class="op">*</span> <span class="ident">_05_05i</span>).<span class="ident">ln</span>(), <span class="ident">_neg1_1i</span>.<span class="ident">ln</span>() <span class="op">+</span> <span class="ident">_05_05i</span>.<span class="ident">ln</span>()));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// ln(conj(z() = conj(ln(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">ln</span>(), <span class="ident">c</span>.<span class="ident">ln</span>().<span class="ident">conj</span>()));
<span class="comment">// for this branch, -pi <= arg(ln(z)) <= pi</span>
<span class="macro">assert!</span>(<span class="op">-</span><span class="ident">f64::consts::PI</span> <span class="op"><</span><span class="op">=</span> <span class="ident">c</span>.<span class="ident">ln</span>().<span class="ident">arg</span>() <span class="op">&&</span> <span class="ident">c</span>.<span class="ident">ln</span>().<span class="ident">arg</span>() <span class="op"><</span><span class="op">=</span> <span class="ident">f64::consts::PI</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_powc</span>()
{
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">2.0</span>, <span class="op">-</span><span class="number">3.0</span>);
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">3.0</span>, <span class="number">0.0</span>);
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">a</span>.<span class="ident">powc</span>(<span class="ident">b</span>), <span class="ident">a</span>.<span class="ident">powf</span>(<span class="ident">b</span>.<span class="ident">re</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">b</span>.<span class="ident">powc</span>(<span class="ident">a</span>), <span class="ident">a</span>.<span class="ident">expf</span>(<span class="ident">b</span>.<span class="ident">re</span>)));
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">1.0</span> <span class="op">/</span> <span class="number">3.0</span>, <span class="number">0.1</span>);
<span class="macro">assert!</span>(<span class="ident">close_to_tol</span>(<span class="ident">a</span>.<span class="ident">powc</span>(<span class="ident">c</span>), <span class="ident">Complex::new</span>(<span class="number">1.65826</span>, <span class="op">-</span><span class="number">0.33502</span>), <span class="number">1e-5</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_powf</span>()
{
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">2.0</span>, <span class="op">-</span><span class="number">1.0</span>);
<span class="kw">let</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">c</span>.<span class="ident">powf</span>(<span class="number">3.5</span>);
<span class="macro">assert!</span>(<span class="ident">close_to_tol</span>(<span class="ident">r</span>, <span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">0.8684746</span>, <span class="op">-</span><span class="number">16.695934</span>), <span class="number">1e-5</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_log</span>()
{
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">2.0</span>, <span class="op">-</span><span class="number">1.0</span>);
<span class="kw">let</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">c</span>.<span class="ident">log</span>(<span class="number">10.0</span>);
<span class="macro">assert!</span>(<span class="ident">close_to_tol</span>(<span class="ident">r</span>, <span class="ident">Complex::new</span>(<span class="number">0.349485</span>, <span class="op">-</span><span class="number">0.20135958</span>), <span class="number">1e-5</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_some_expf_cases</span>()
{
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">2.0</span>, <span class="op">-</span><span class="number">1.0</span>);
<span class="kw">let</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">c</span>.<span class="ident">expf</span>(<span class="number">10.0</span>);
<span class="macro">assert!</span>(<span class="ident">close_to_tol</span>(<span class="ident">r</span>, <span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">66.82015</span>, <span class="op">-</span><span class="number">74.39803</span>), <span class="number">1e-5</span>));
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">5.0</span>, <span class="op">-</span><span class="number">2.0</span>);
<span class="kw">let</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">c</span>.<span class="ident">expf</span>(<span class="number">3.4</span>);
<span class="macro">assert!</span>(<span class="ident">close_to_tol</span>(<span class="ident">r</span>, <span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">349.25</span>, <span class="op">-</span><span class="number">290.63</span>), <span class="number">1e-2</span>));
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">1.5</span>, <span class="number">2.0</span> <span class="op">/</span> <span class="number">3.0</span>);
<span class="kw">let</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">c</span>.<span class="ident">expf</span>(<span class="number">1.0</span> <span class="op">/</span> <span class="number">3.0</span>);
<span class="macro">assert!</span>(<span class="ident">close_to_tol</span>(<span class="ident">r</span>, <span class="ident">Complex::new</span>(<span class="number">3.8637</span>, <span class="op">-</span><span class="number">3.4745</span>), <span class="number">1e-2</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_sqrt</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">sqrt</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">sqrt</span>(), <span class="ident">_1_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">1.0</span>, <span class="number">0.0</span>).<span class="ident">sqrt</span>(), <span class="ident">_0_1i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">1.0</span>, <span class="op">-</span><span class="number">0.0</span>).<span class="ident">sqrt</span>(), <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">sqrt</span>(), <span class="ident">_05_05i</span>.<span class="ident">scale</span>(<span class="number">2.0</span>.<span class="ident">sqrt</span>())));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// sqrt(conj(z() = conj(sqrt(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">sqrt</span>(), <span class="ident">c</span>.<span class="ident">sqrt</span>().<span class="ident">conj</span>()));
<span class="comment">// for this branch, -pi/2 <= arg(sqrt(z)) <= pi/2</span>
<span class="macro">assert!</span>(<span class="op">-</span><span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span> <span class="op"><</span><span class="op">=</span> <span class="ident">c</span>.<span class="ident">sqrt</span>().<span class="ident">arg</span>() <span class="op">&&</span> <span class="ident">c</span>.<span class="ident">sqrt</span>().<span class="ident">arg</span>() <span class="op"><</span><span class="op">=</span> <span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>);
<span class="comment">// sqrt(z) * sqrt(z) = z</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">sqrt</span>()<span class="kw-2">*</span><span class="ident">c</span>.<span class="ident">sqrt</span>(), <span class="ident">c</span>));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_sin</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">sin</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="kw-2">*</span><span class="number">2.0</span>).<span class="ident">sin</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">sin</span>(), <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="number">1.0</span>.<span class="ident">sinh</span>())));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// sin(conj(z)) = conj(sin(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">sin</span>(), <span class="ident">c</span>.<span class="ident">sin</span>().<span class="ident">conj</span>()));
<span class="comment">// sin(-z) = -sin(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">sin</span>(), <span class="ident">c</span>.<span class="ident">sin</span>().<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>)));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_cos</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">cos</span>(), <span class="ident">_1_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="kw-2">*</span><span class="number">2.0</span>).<span class="ident">cos</span>(), <span class="ident">_1_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">cos</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="number">1.0</span>.<span class="ident">cosh</span>())));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// cos(conj(z)) = conj(cos(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">cos</span>(), <span class="ident">c</span>.<span class="ident">cos</span>().<span class="ident">conj</span>()));
<span class="comment">// cos(-z) = cos(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">cos</span>(), <span class="ident">c</span>.<span class="ident">cos</span>()));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_tan</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">tan</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">4.0</span>).<span class="ident">tan</span>(), <span class="ident">_1_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span>).<span class="ident">tan</span>(), <span class="ident">_0_0i</span>));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// tan(conj(z)) = conj(tan(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">tan</span>(), <span class="ident">c</span>.<span class="ident">tan</span>().<span class="ident">conj</span>()));
<span class="comment">// tan(-z) = -tan(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">tan</span>(), <span class="ident">c</span>.<span class="ident">tan</span>().<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>)));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_asin</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">asin</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">asin</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">asin</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">asin</span>(), <span class="ident">_0_1i</span>.<span class="ident">scale</span>((<span class="number">1.0</span> <span class="op">+</span> <span class="number">2.0</span>.<span class="ident">sqrt</span>()).<span class="ident">ln</span>())));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// asin(conj(z)) = conj(asin(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">asin</span>(), <span class="ident">c</span>.<span class="ident">asin</span>().<span class="ident">conj</span>()));
<span class="comment">// asin(-z) = -asin(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">asin</span>(), <span class="ident">c</span>.<span class="ident">asin</span>().<span class="ident">scale</span>(<span class="op">-</span><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>(<span class="op">-</span><span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span> <span class="op"><</span><span class="op">=</span> <span class="ident">c</span>.<span class="ident">asin</span>().<span class="ident">re</span> <span class="op">&&</span> <span class="ident">c</span>.<span class="ident">asin</span>().<span class="ident">re</span> <span class="op"><</span><span class="op">=</span> <span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_acos</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">acos</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">acos</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">acos</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">acos</span>(), <span class="ident">Complex::new</span>(<span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>, (<span class="number">2.0</span>.<span class="ident">sqrt</span>() <span class="op">-</span> <span class="number">1.0</span>).<span class="ident">ln</span>())));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// acos(conj(z)) = conj(acos(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">acos</span>(), <span class="ident">c</span>.<span class="ident">acos</span>().<span class="ident">conj</span>()));
<span class="comment">// for this branch, 0 <= acos(z).re <= pi</span>
<span class="macro">assert!</span>(<span class="number">0.0</span> <span class="op"><</span><span class="op">=</span> <span class="ident">c</span>.<span class="ident">acos</span>().<span class="ident">re</span> <span class="op">&&</span> <span class="ident">c</span>.<span class="ident">acos</span>().<span class="ident">re</span> <span class="op"><</span><span class="op">=</span> <span class="ident">f64::consts::PI</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_atan</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">atan</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">atan</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">4.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">atan</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">4.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">atan</span>(), <span class="ident">Complex::new</span>(<span class="number">0.0</span>, <span class="ident">f64::infinity</span>())));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// atan(conj(z)) = conj(atan(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">atan</span>(), <span class="ident">c</span>.<span class="ident">atan</span>().<span class="ident">conj</span>()));
<span class="comment">// atan(-z) = -atan(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">atan</span>(), <span class="ident">c</span>.<span class="ident">atan</span>().<span class="ident">scale</span>(<span class="op">-</span><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>(<span class="op">-</span><span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span> <span class="op"><</span><span class="op">=</span> <span class="ident">c</span>.<span class="ident">atan</span>().<span class="ident">re</span> <span class="op">&&</span> <span class="ident">c</span>.<span class="ident">atan</span>().<span class="ident">re</span> <span class="op"><</span><span class="op">=</span> <span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_sinh</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">sinh</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">sinh</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>((<span class="ident">f64::consts::E</span> <span class="op">-</span> <span class="number">1.0</span><span class="op">/</span><span class="ident">f64::consts::E</span>)<span class="op">/</span><span class="number">2.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">sinh</span>(), <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="number">1.0</span>.<span class="ident">sin</span>())));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// sinh(conj(z)) = conj(sinh(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">sinh</span>(), <span class="ident">c</span>.<span class="ident">sinh</span>().<span class="ident">conj</span>()));
<span class="comment">// sinh(-z) = -sinh(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">sinh</span>(), <span class="ident">c</span>.<span class="ident">sinh</span>().<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>)));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_cosh</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">cosh</span>(), <span class="ident">_1_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">cosh</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>((<span class="ident">f64::consts::E</span> <span class="op">+</span> <span class="number">1.0</span><span class="op">/</span><span class="ident">f64::consts::E</span>)<span class="op">/</span><span class="number">2.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">cosh</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="number">1.0</span>.<span class="ident">cos</span>())));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// cosh(conj(z)) = conj(cosh(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">cosh</span>(), <span class="ident">c</span>.<span class="ident">cosh</span>().<span class="ident">conj</span>()));
<span class="comment">// cosh(-z) = cosh(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">cosh</span>(), <span class="ident">c</span>.<span class="ident">cosh</span>()));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_tanh</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">tanh</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">tanh</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>((<span class="ident">f64::consts::E</span>.<span class="ident">powi</span>(<span class="number">2</span>) <span class="op">-</span> <span class="number">1.0</span>)<span class="op">/</span>(<span class="ident">f64::consts::E</span>.<span class="ident">powi</span>(<span class="number">2</span>) <span class="op">+</span> <span class="number">1.0</span>))));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">tanh</span>(), <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="number">1.0</span>.<span class="ident">tan</span>())));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// tanh(conj(z)) = conj(tanh(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">tanh</span>(), <span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">tanh</span>()));
<span class="comment">// tanh(-z) = -tanh(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">tanh</span>(), <span class="ident">c</span>.<span class="ident">tanh</span>().<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>)));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_asinh</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">asinh</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">asinh</span>(), <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="number">1.0</span> <span class="op">+</span> <span class="number">2.0</span>.<span class="ident">sqrt</span>()).<span class="ident">ln</span>()));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">asinh</span>(), <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">asinh</span>().<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>), <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>)));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// asinh(conj(z)) = conj(asinh(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">asinh</span>(), <span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">asinh</span>()));
<span class="comment">// asinh(-z) = -asinh(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">asinh</span>(), <span class="ident">c</span>.<span class="ident">asinh</span>().<span class="ident">scale</span>(<span class="op">-</span><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>(<span class="op">-</span><span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span> <span class="op"><</span><span class="op">=</span> <span class="ident">c</span>.<span class="ident">asinh</span>().<span class="ident">im</span> <span class="op">&&</span> <span class="ident">c</span>.<span class="ident">asinh</span>().<span class="ident">im</span> <span class="op"><</span><span class="op">=</span> <span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_acosh</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">acosh</span>(), <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">acosh</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">acosh</span>(), <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span>)));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// acosh(conj(z)) = conj(acosh(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">acosh</span>(), <span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">acosh</span>()));
<span class="comment">// for this branch, -pi <= acosh(z).im <= pi and 0 <= acosh(z).re</span>
<span class="macro">assert!</span>(<span class="op">-</span><span class="ident">f64::consts::PI</span> <span class="op"><</span><span class="op">=</span> <span class="ident">c</span>.<span class="ident">acosh</span>().<span class="ident">im</span> <span class="op">&&</span> <span class="ident">c</span>.<span class="ident">acosh</span>().<span class="ident">im</span> <span class="op"><</span><span class="op">=</span> <span class="ident">f64::consts::PI</span> <span class="op">&&</span> <span class="number">0.0</span> <span class="op"><</span><span class="op">=</span> <span class="ident">c</span>.<span class="ident">cosh</span>().<span class="ident">re</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_atanh</span>() {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_0i</span>.<span class="ident">atanh</span>(), <span class="ident">_0_0i</span>));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span>.<span class="ident">atanh</span>(), <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">4.0</span>)));
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_1_0i</span>.<span class="ident">atanh</span>(), <span class="ident">Complex::new</span>(<span class="ident">f64::infinity</span>(), <span class="number">0.0</span>)));
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// atanh(conj(z)) = conj(atanh(z))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">atanh</span>(), <span class="ident">c</span>.<span class="ident">conj</span>().<span class="ident">atanh</span>()));
<span class="comment">// atanh(-z) = -atanh(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">atanh</span>(), <span class="ident">c</span>.<span class="ident">atanh</span>().<span class="ident">scale</span>(<span class="op">-</span><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>(<span class="op">-</span><span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span> <span class="op"><</span><span class="op">=</span> <span class="ident">c</span>.<span class="ident">atanh</span>().<span class="ident">im</span> <span class="op">&&</span> <span class="ident">c</span>.<span class="ident">atanh</span>().<span class="ident">im</span> <span class="op"><</span><span class="op">=</span> <span class="ident">f64::consts::PI</span><span class="op">/</span><span class="number">2.0</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_exp_ln</span>() {
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// e^ln(z) = z</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">ln</span>().<span class="ident">exp</span>(), <span class="ident">c</span>));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_trig_to_hyperbolic</span>() {
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// sin(iz) = i sinh(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>((<span class="ident">_0_1i</span> <span class="op">*</span> <span class="ident">c</span>).<span class="ident">sin</span>(), <span class="ident">_0_1i</span> <span class="op">*</span> <span class="ident">c</span>.<span class="ident">sinh</span>()));
<span class="comment">// cos(iz) = cosh(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>((<span class="ident">_0_1i</span> <span class="op">*</span> <span class="ident">c</span>).<span class="ident">cos</span>(), <span class="ident">c</span>.<span class="ident">cosh</span>()));
<span class="comment">// tan(iz) = i tanh(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>((<span class="ident">_0_1i</span> <span class="op">*</span> <span class="ident">c</span>).<span class="ident">tan</span>(), <span class="ident">_0_1i</span> <span class="op">*</span> <span class="ident">c</span>.<span class="ident">tanh</span>()));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_trig_identities</span>() {
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// tan(z) = sin(z)/cos(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">tan</span>(), <span class="ident">c</span>.<span class="ident">sin</span>()<span class="op">/</span><span class="ident">c</span>.<span class="ident">cos</span>()));
<span class="comment">// sin(z)^2 + cos(z)^2 = 1</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">sin</span>()<span class="kw-2">*</span><span class="ident">c</span>.<span class="ident">sin</span>() <span class="op">+</span> <span class="ident">c</span>.<span class="ident">cos</span>()<span class="kw-2">*</span><span class="ident">c</span>.<span class="ident">cos</span>(), <span class="ident">_1_0i</span>));
<span class="comment">// sin(asin(z)) = z</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">asin</span>().<span class="ident">sin</span>(), <span class="ident">c</span>));
<span class="comment">// cos(acos(z)) = z</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">acos</span>().<span class="ident">cos</span>(), <span class="ident">c</span>));
<span class="comment">// tan(atan(z)) = z</span>
<span class="comment">// i and -i are branch points</span>
<span class="kw">if</span> <span class="ident">c</span> <span class="op">!</span><span class="op">=</span> <span class="ident">_0_1i</span> <span class="op">&&</span> <span class="ident">c</span> <span class="op">!</span><span class="op">=</span> <span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>) {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">atan</span>().<span class="ident">tan</span>(), <span class="ident">c</span>));
}
<span class="comment">// sin(z) = (e^(iz) - e^(-iz))/(2i)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(((<span class="ident">_0_1i</span><span class="kw-2">*</span><span class="ident">c</span>).<span class="ident">exp</span>() <span class="op">-</span> (<span class="ident">_0_1i</span><span class="kw-2">*</span><span class="ident">c</span>).<span class="ident">exp</span>().<span class="ident">inv</span>())<span class="op">/</span><span class="ident">_0_1i</span>.<span class="ident">scale</span>(<span class="number">2.0</span>), <span class="ident">c</span>.<span class="ident">sin</span>()));
<span class="comment">// cos(z) = (e^(iz) + e^(-iz))/2</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(((<span class="ident">_0_1i</span><span class="kw-2">*</span><span class="ident">c</span>).<span class="ident">exp</span>() <span class="op">+</span> (<span class="ident">_0_1i</span><span class="kw-2">*</span><span class="ident">c</span>).<span class="ident">exp</span>().<span class="ident">inv</span>()).<span class="ident">unscale</span>(<span class="number">2.0</span>), <span class="ident">c</span>.<span class="ident">cos</span>()));
<span class="comment">// tan(z) = i (1 - e^(2iz))/(1 + e^(2iz))</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">_0_1i</span> <span class="op">*</span> (<span class="ident">_1_0i</span> <span class="op">-</span> (<span class="ident">_0_1i</span><span class="kw-2">*</span><span class="ident">c</span>).<span class="ident">scale</span>(<span class="number">2.0</span>).<span class="ident">exp</span>())<span class="op">/</span>(<span class="ident">_1_0i</span> <span class="op">+</span> (<span class="ident">_0_1i</span><span class="kw-2">*</span><span class="ident">c</span>).<span class="ident">scale</span>(<span class="number">2.0</span>).<span class="ident">exp</span>()), <span class="ident">c</span>.<span class="ident">tan</span>()));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_hyperbolic_identites</span>() {
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="comment">// tanh(z) = sinh(z)/cosh(z)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">tanh</span>(), <span class="ident">c</span>.<span class="ident">sinh</span>()<span class="op">/</span><span class="ident">c</span>.<span class="ident">cosh</span>()));
<span class="comment">// cosh(z)^2 - sinh(z)^2 = 1</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">cosh</span>()<span class="kw-2">*</span><span class="ident">c</span>.<span class="ident">cosh</span>() <span class="op">-</span> <span class="ident">c</span>.<span class="ident">sinh</span>()<span class="kw-2">*</span><span class="ident">c</span>.<span class="ident">sinh</span>(), <span class="ident">_1_0i</span>));
<span class="comment">// sinh(asinh(z)) = z</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">asinh</span>().<span class="ident">sinh</span>(), <span class="ident">c</span>));
<span class="comment">// cosh(acosh(z)) = z</span>
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">acosh</span>().<span class="ident">cosh</span>(), <span class="ident">c</span>));
<span class="comment">// tanh(atanh(z)) = z</span>
<span class="comment">// 1 and -1 are branch points</span>
<span class="kw">if</span> <span class="ident">c</span> <span class="op">!</span><span class="op">=</span> <span class="ident">_1_0i</span> <span class="op">&&</span> <span class="ident">c</span> <span class="op">!</span><span class="op">=</span> <span class="ident">_1_0i</span>.<span class="ident">scale</span>(<span class="op">-</span><span class="number">1.0</span>) {
<span class="macro">assert!</span>(<span class="ident">close</span>(<span class="ident">c</span>.<span class="ident">atanh</span>().<span class="ident">tanh</span>(), <span class="ident">c</span>));
}
<span class="comment">// sinh(z) = (e^z - e^(-z))/2</span>
<span class="macro">assert!</span>(<span class="ident">close</span>((<span class="ident">c</span>.<span class="ident">exp</span>() <span class="op">-</span> <span class="ident">c</span>.<span class="ident">exp</span>().<span class="ident">inv</span>()).<span class="ident">unscale</span>(<span class="number">2.0</span>), <span class="ident">c</span>.<span class="ident">sinh</span>()));
<span class="comment">// cosh(z) = (e^z + e^(-z))/2</span>
<span class="macro">assert!</span>(<span class="ident">close</span>((<span class="ident">c</span>.<span class="ident">exp</span>() <span class="op">+</span> <span class="ident">c</span>.<span class="ident">exp</span>().<span class="ident">inv</span>()).<span class="ident">unscale</span>(<span class="number">2.0</span>), <span class="ident">c</span>.<span class="ident">cosh</span>()));
<span class="comment">// tanh(z) = ( e^(2z) - 1)/(e^(2z) + 1)</span>
<span class="macro">assert!</span>(<span class="ident">close</span>((<span class="ident">c</span>.<span class="ident">scale</span>(<span class="number">2.0</span>).<span class="ident">exp</span>() <span class="op">-</span> <span class="ident">_1_0i</span>)<span class="op">/</span>(<span class="ident">c</span>.<span class="ident">scale</span>(<span class="number">2.0</span>).<span class="ident">exp</span>() <span class="op">+</span> <span class="ident">_1_0i</span>), <span class="ident">c</span>.<span class="ident">tanh</span>()));
}
}
<span class="comment">// Test both a + b and a += b</span>
<span class="macro">macro_rules!</span> <span class="ident">test_a_op_b</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>:<span class="ident">ident</span> <span class="op">+</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {
<span class="macro">assert_eq!</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span> <span class="op">+</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
<span class="macro">assert_eq!</span>({ <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">x</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>; <span class="ident">x</span> <span class="op">+</span><span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>; <span class="ident">x</span>}, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
};
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>:<span class="ident">ident</span> <span class="op">-</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {
<span class="macro">assert_eq!</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span> <span class="op">-</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
<span class="macro">assert_eq!</span>({ <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">x</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>; <span class="ident">x</span> <span class="op">-</span><span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>; <span class="ident">x</span>}, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
};
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>:<span class="ident">ident</span> <span class="op">*</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {
<span class="macro">assert_eq!</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span> <span class="op">*</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
<span class="macro">assert_eq!</span>({ <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">x</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>; <span class="ident">x</span> <span class="kw-2">*</span><span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>; <span class="ident">x</span>}, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
};
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>:<span class="ident">ident</span> <span class="op">/</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {
<span class="macro">assert_eq!</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span> <span class="op">/</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
<span class="macro">assert_eq!</span>({ <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">x</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>; <span class="ident">x</span> <span class="op">/</span><span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>; <span class="ident">x</span>}, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
};
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>:<span class="ident">ident</span> <span class="op">%</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {
<span class="macro">assert_eq!</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span> <span class="op">%</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
<span class="macro">assert_eq!</span>({ <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">x</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>; <span class="ident">x</span> <span class="op">%</span><span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>; <span class="ident">x</span>}, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
}
}
<span class="comment">// Test both a + b and a + &b</span>
<span class="macro">macro_rules!</span> <span class="ident">test_op</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>:<span class="ident">ident</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">op</span>:<span class="ident">tt</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {
<span class="macro">test_a_op_b!</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">op</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
<span class="macro">test_a_op_b!</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">op</span> <span class="kw-2">&</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">answer</span>);
}
}
<span class="kw">mod</span> <span class="ident">complex_arithmetic</span> {
<span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">_0_0i</span>, <span class="ident">_1_0i</span>, <span class="ident">_1_1i</span>, <span class="ident">_0_1i</span>, <span class="ident">_neg1_1i</span>, <span class="ident">_05_05i</span>, <span class="ident">_4_2i</span>, <span class="ident">all_consts</span>};
<span class="kw">use</span> <span class="ident">traits::Zero</span>;
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_add</span>() {
<span class="macro">test_op!</span>(<span class="ident">_05_05i</span> <span class="op">+</span> <span class="ident">_05_05i</span>, <span class="ident">_1_1i</span>);
<span class="macro">test_op!</span>(<span class="ident">_0_1i</span> <span class="op">+</span> <span class="ident">_1_0i</span>, <span class="ident">_1_1i</span>);
<span class="macro">test_op!</span>(<span class="ident">_1_0i</span> <span class="op">+</span> <span class="ident">_neg1_1i</span>, <span class="ident">_0_1i</span>);
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="macro">test_op!</span>(<span class="ident">_0_0i</span> <span class="op">+</span> <span class="ident">c</span>, <span class="ident">c</span>);
<span class="macro">test_op!</span>(<span class="ident">c</span> <span class="op">+</span> <span class="ident">_0_0i</span>, <span class="ident">c</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_sub</span>() {
<span class="macro">test_op!</span>(<span class="ident">_05_05i</span> <span class="op">-</span> <span class="ident">_05_05i</span>, <span class="ident">_0_0i</span>);
<span class="macro">test_op!</span>(<span class="ident">_0_1i</span> <span class="op">-</span> <span class="ident">_1_0i</span>, <span class="ident">_neg1_1i</span>);
<span class="macro">test_op!</span>(<span class="ident">_0_1i</span> <span class="op">-</span> <span class="ident">_neg1_1i</span>, <span class="ident">_1_0i</span>);
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="macro">test_op!</span>(<span class="ident">c</span> <span class="op">-</span> <span class="ident">_0_0i</span>, <span class="ident">c</span>);
<span class="macro">test_op!</span>(<span class="ident">c</span> <span class="op">-</span> <span class="ident">c</span>, <span class="ident">_0_0i</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_mul</span>() {
<span class="macro">test_op!</span>(<span class="ident">_05_05i</span> <span class="op">*</span> <span class="ident">_05_05i</span>, <span class="ident">_0_1i</span>.<span class="ident">unscale</span>(<span class="number">2.0</span>));
<span class="macro">test_op!</span>(<span class="ident">_1_1i</span> <span class="op">*</span> <span class="ident">_0_1i</span>, <span class="ident">_neg1_1i</span>);
<span class="comment">// i^2 & i^4</span>
<span class="macro">test_op!</span>(<span class="ident">_0_1i</span> <span class="op">*</span> <span class="ident">_0_1i</span>, <span class="op">-</span><span class="ident">_1_0i</span>);
<span class="macro">assert_eq!</span>(<span class="ident">_0_1i</span> <span class="op">*</span> <span class="ident">_0_1i</span> <span class="op">*</span> <span class="ident">_0_1i</span> <span class="op">*</span> <span class="ident">_0_1i</span>, <span class="ident">_1_0i</span>);
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="macro">test_op!</span>(<span class="ident">c</span> <span class="op">*</span> <span class="ident">_1_0i</span>, <span class="ident">c</span>);
<span class="macro">test_op!</span>(<span class="ident">_1_0i</span> <span class="op">*</span> <span class="ident">c</span>, <span class="ident">c</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_div</span>() {
<span class="macro">test_op!</span>(<span class="ident">_neg1_1i</span> <span class="op">/</span> <span class="ident">_0_1i</span>, <span class="ident">_1_1i</span>);
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="kw">if</span> <span class="ident">c</span> <span class="op">!</span><span class="op">=</span> <span class="ident">Zero::zero</span>() {
<span class="macro">test_op!</span>(<span class="ident">c</span> <span class="op">/</span> <span class="ident">c</span>, <span class="ident">_1_0i</span>);
}
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_rem</span>() {
<span class="macro">test_op!</span>(<span class="ident">_neg1_1i</span> <span class="op">%</span> <span class="ident">_0_1i</span>, <span class="ident">_0_0i</span>);
<span class="macro">test_op!</span>(<span class="ident">_4_2i</span> <span class="op">%</span> <span class="ident">_0_1i</span>, <span class="ident">_0_0i</span>);
<span class="macro">test_op!</span>(<span class="ident">_05_05i</span> <span class="op">%</span> <span class="ident">_0_1i</span>, <span class="ident">_05_05i</span>);
<span class="macro">test_op!</span>(<span class="ident">_05_05i</span> <span class="op">%</span> <span class="ident">_1_1i</span>, <span class="ident">_05_05i</span>);
<span class="macro">assert_eq!</span>((<span class="ident">_4_2i</span> <span class="op">+</span> <span class="ident">_05_05i</span>) <span class="op">%</span> <span class="ident">_0_1i</span>, <span class="ident">_05_05i</span>);
<span class="macro">assert_eq!</span>((<span class="ident">_4_2i</span> <span class="op">+</span> <span class="ident">_05_05i</span>) <span class="op">%</span> <span class="ident">_1_1i</span>, <span class="ident">_05_05i</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_neg</span>() {
<span class="macro">assert_eq!</span>(<span class="op">-</span><span class="ident">_1_0i</span> <span class="op">+</span> <span class="ident">_0_1i</span>, <span class="ident">_neg1_1i</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="ident">_0_1i</span>) <span class="op">*</span> <span class="ident">_0_1i</span>, <span class="ident">_1_0i</span>);
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">c</span> <span class="kw">in</span> <span class="ident">all_consts</span>.<span class="ident">iter</span>() {
<span class="macro">assert_eq!</span>(<span class="op">-</span>(<span class="op">-</span><span class="ident">c</span>), <span class="ident">c</span>);
}
}
}
<span class="kw">mod</span> <span class="ident">real_arithmetic</span> {
<span class="kw">use</span> <span class="kw">super</span>::<span class="kw">super</span><span class="ident">::Complex</span>;
<span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">_4_2i</span>, <span class="ident">_neg1_1i</span>};
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_add</span>() {
<span class="macro">test_op!</span>(<span class="ident">_4_2i</span> <span class="op">+</span> <span class="number">0.5</span>, <span class="ident">Complex::new</span>(<span class="number">4.5</span>, <span class="number">2.0</span>));
<span class="macro">assert_eq!</span>(<span class="number">0.5</span> <span class="op">+</span> <span class="ident">_4_2i</span>, <span class="ident">Complex::new</span>(<span class="number">4.5</span>, <span class="number">2.0</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_sub</span>() {
<span class="macro">test_op!</span>(<span class="ident">_4_2i</span> <span class="op">-</span> <span class="number">0.5</span>, <span class="ident">Complex::new</span>(<span class="number">3.5</span>, <span class="number">2.0</span>));
<span class="macro">assert_eq!</span>(<span class="number">0.5</span> <span class="op">-</span> <span class="ident">_4_2i</span>, <span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">3.5</span>, <span class="op">-</span><span class="number">2.0</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_mul</span>() {
<span class="macro">assert_eq!</span>(<span class="ident">_4_2i</span> <span class="op">*</span> <span class="number">0.5</span>, <span class="ident">Complex::new</span>(<span class="number">2.0</span>, <span class="number">1.0</span>));
<span class="macro">assert_eq!</span>(<span class="number">0.5</span> <span class="op">*</span> <span class="ident">_4_2i</span>, <span class="ident">Complex::new</span>(<span class="number">2.0</span>, <span class="number">1.0</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_div</span>() {
<span class="macro">assert_eq!</span>(<span class="ident">_4_2i</span> <span class="op">/</span> <span class="number">0.5</span>, <span class="ident">Complex::new</span>(<span class="number">8.0</span>, <span class="number">4.0</span>));
<span class="macro">assert_eq!</span>(<span class="number">0.5</span> <span class="op">/</span> <span class="ident">_4_2i</span>, <span class="ident">Complex::new</span>(<span class="number">0.1</span>, <span class="op">-</span><span class="number">0.05</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_rem</span>() {
<span class="macro">assert_eq!</span>(<span class="ident">_4_2i</span> <span class="op">%</span> <span class="number">2.0</span>, <span class="ident">Complex::new</span>(<span class="number">0.0</span>, <span class="number">0.0</span>));
<span class="macro">assert_eq!</span>(<span class="ident">_4_2i</span> <span class="op">%</span> <span class="number">3.0</span>, <span class="ident">Complex::new</span>(<span class="number">1.0</span>, <span class="number">2.0</span>));
<span class="macro">assert_eq!</span>(<span class="number">3.0</span> <span class="op">%</span> <span class="ident">_4_2i</span>, <span class="ident">Complex::new</span>(<span class="number">3.0</span>, <span class="number">0.0</span>));
<span class="macro">assert_eq!</span>(<span class="ident">_neg1_1i</span> <span class="op">%</span> <span class="number">2.0</span>, <span class="ident">_neg1_1i</span>);
<span class="macro">assert_eq!</span>(<span class="op">-</span><span class="ident">_4_2i</span> <span class="op">%</span> <span class="number">3.0</span>, <span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">1.0</span>, <span class="op">-</span><span class="number">2.0</span>));
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_to_string</span>() {
<span class="kw">fn</span> <span class="ident">test</span>(<span class="ident">c</span> : <span class="ident">Complex64</span>, <span class="ident">s</span>: <span class="ident">String</span>) {
<span class="macro">assert_eq!</span>(<span class="ident">c</span>.<span class="ident">to_string</span>(), <span class="ident">s</span>);
}
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"0+0i"</span>.<span class="ident">to_string</span>());
<span class="ident">test</span>(<span class="ident">_1_0i</span>, <span class="string">"1+0i"</span>.<span class="ident">to_string</span>());
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"0+1i"</span>.<span class="ident">to_string</span>());
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="string">"1+1i"</span>.<span class="ident">to_string</span>());
<span class="ident">test</span>(<span class="ident">_neg1_1i</span>, <span class="string">"-1+1i"</span>.<span class="ident">to_string</span>());
<span class="ident">test</span>(<span class="op">-</span><span class="ident">_neg1_1i</span>, <span class="string">"1-1i"</span>.<span class="ident">to_string</span>());
<span class="ident">test</span>(<span class="ident">_05_05i</span>, <span class="string">"0.5+0.5i"</span>.<span class="ident">to_string</span>());
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_string_formatting</span>() {
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<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>, <span class="ident">a</span>), <span class="string">"1.23456+123.456i"</span>);
<span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:.2}"</span>, <span class="ident">a</span>), <span class="string">"1.23+123.46i"</span>);
<span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:.2e}"</span>, <span class="ident">a</span>), <span class="string">"1.23e0+1.23e2i"</span>);
<span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:+20.2E}"</span>, <span class="ident">a</span>), <span class="string">" +1.23E0+1.23E2i"</span>);
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<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>, <span class="ident">b</span>), <span class="string">"80+FFi"</span>);
<span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:#x}"</span>, <span class="ident">b</span>), <span class="string">"0x80+0xffi"</span>);
<span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:+#b}"</span>, <span class="ident">b</span>), <span class="string">"+0b10000000+0b11111111i"</span>);
<span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:+#16o}"</span>, <span class="ident">b</span>), <span class="string">" +0o200+0o377i"</span>);
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">10</span>, <span class="op">-</span><span class="number">10000</span>);
<span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{}"</span>, <span class="ident">c</span>), <span class="string">"-10-10000i"</span>);
<span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:16}"</span>, <span class="ident">c</span>), <span class="string">" -10-10000i"</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_hash</span>() {
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">0i32</span>, <span class="number">0i32</span>);
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">1i32</span>, <span class="number">0i32</span>);
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">0i32</span>, <span class="number">1i32</span>);
<span class="macro">assert!</span>(<span class="ident">::hash</span>(<span class="kw-2">&</span><span class="ident">a</span>) <span class="op">!</span><span class="op">=</span> <span class="ident">::hash</span>(<span class="kw-2">&</span><span class="ident">b</span>));
<span class="macro">assert!</span>(<span class="ident">::hash</span>(<span class="kw-2">&</span><span class="ident">b</span>) <span class="op">!</span><span class="op">=</span> <span class="ident">::hash</span>(<span class="kw-2">&</span><span class="ident">c</span>));
<span class="macro">assert!</span>(<span class="ident">::hash</span>(<span class="kw-2">&</span><span class="ident">c</span>) <span class="op">!</span><span class="op">=</span> <span class="ident">::hash</span>(<span class="kw-2">&</span><span class="ident">a</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_hashset</span>() {
<span class="kw">use</span> <span class="ident">std::collections::HashSet</span>;
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">0i32</span>, <span class="number">0i32</span>);
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">1i32</span>, <span class="number">0i32</span>);
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">0i32</span>, <span class="number">1i32</span>);
<span class="kw">let</span> <span class="ident">set</span>: <span class="ident">HashSet</span><span class="op"><</span><span class="kw">_</span><span class="op">></span> <span class="op">=</span> [<span class="ident">a</span>, <span class="ident">b</span>, <span class="ident">c</span>].<span class="ident">iter</span>().<span class="ident">cloned</span>().<span class="ident">collect</span>();
<span class="macro">assert!</span>(<span class="ident">set</span>.<span class="ident">contains</span>(<span class="kw-2">&</span><span class="ident">a</span>));
<span class="macro">assert!</span>(<span class="ident">set</span>.<span class="ident">contains</span>(<span class="kw-2">&</span><span class="ident">b</span>));
<span class="macro">assert!</span>(<span class="ident">set</span>.<span class="ident">contains</span>(<span class="kw-2">&</span><span class="ident">c</span>));
<span class="macro">assert!</span>(<span class="op">!</span><span class="ident">set</span>.<span class="ident">contains</span>(<span class="kw-2">&</span>(<span class="ident">a</span> <span class="op">+</span> <span class="ident">b</span> <span class="op">+</span> <span class="ident">c</span>)));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_is_nan</span>() {
<span class="macro">assert!</span>(<span class="op">!</span><span class="ident">_1_1i</span>.<span class="ident">is_nan</span>());
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="ident">f64::NAN</span>, <span class="ident">f64::NAN</span>);
<span class="macro">assert!</span>(<span class="ident">a</span>.<span class="ident">is_nan</span>());
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_is_nan_special_cases</span>() {
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">0f64</span>, <span class="ident">f64::NAN</span>);
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="ident">f64::NAN</span>, <span class="number">0f64</span>);
<span class="macro">assert!</span>(<span class="ident">a</span>.<span class="ident">is_nan</span>());
<span class="macro">assert!</span>(<span class="ident">b</span>.<span class="ident">is_nan</span>());
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_is_infinite</span>() {
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">2f64</span>, <span class="ident">f64::INFINITY</span>);
<span class="macro">assert!</span>(<span class="ident">a</span>.<span class="ident">is_infinite</span>());
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_is_finite</span>() {
<span class="macro">assert!</span>(<span class="ident">_1_1i</span>.<span class="ident">is_finite</span>())
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_is_normal</span>() {
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">0f64</span>, <span class="ident">f64::NAN</span>);
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="ident">Complex::new</span>(<span class="number">2f64</span>, <span class="ident">f64::INFINITY</span>);
<span class="macro">assert!</span>(<span class="op">!</span><span class="ident">a</span>.<span class="ident">is_normal</span>());
<span class="macro">assert!</span>(<span class="op">!</span><span class="ident">b</span>.<span class="ident">is_normal</span>());
<span class="macro">assert!</span>(<span class="ident">_1_1i</span>.<span class="ident">is_normal</span>());
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_from_str</span>() {
<span class="kw">fn</span> <span class="ident">test</span>(<span class="ident">z</span>: <span class="ident">Complex64</span>, <span class="ident">s</span>: <span class="kw-2">&</span><span class="ident">str</span>) {
<span class="macro">assert_eq!</span>(<span class="ident">FromStr::from_str</span>(<span class="ident">s</span>), <span class="prelude-val">Ok</span>(<span class="ident">z</span>));
}
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"0 + 0i"</span>);
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"0+0j"</span>);
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"0 - 0j"</span>);
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"0-0i"</span>);
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"0i + 0"</span>);
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"0"</span>);
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"-0"</span>);
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"0i"</span>);
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"0j"</span>);
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"+0j"</span>);
<span class="ident">test</span>(<span class="ident">_0_0i</span>, <span class="string">"-0i"</span>);
<span class="ident">test</span>(<span class="ident">_1_0i</span>, <span class="string">"1 + 0i"</span>);
<span class="ident">test</span>(<span class="ident">_1_0i</span>, <span class="string">"1+0j"</span>);
<span class="ident">test</span>(<span class="ident">_1_0i</span>, <span class="string">"1 - 0j"</span>);
<span class="ident">test</span>(<span class="ident">_1_0i</span>, <span class="string">"+1-0i"</span>);
<span class="ident">test</span>(<span class="ident">_1_0i</span>, <span class="string">"-0j+1"</span>);
<span class="ident">test</span>(<span class="ident">_1_0i</span>, <span class="string">"1"</span>);
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="string">"1 + i"</span>);
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="string">"1+j"</span>);
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="string">"1 + 1j"</span>);
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="string">"1+1i"</span>);
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="string">"i + 1"</span>);
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="string">"1i+1"</span>);
<span class="ident">test</span>(<span class="ident">_1_1i</span>, <span class="string">"+j+1"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"0 + i"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"0+j"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"-0 + j"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"-0+i"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"0 + 1i"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"0+1j"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"-0 + 1j"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"-0+1i"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"j + 0"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"i"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"j"</span>);
<span class="ident">test</span>(<span class="ident">_0_1i</span>, <span class="string">"1j"</span>);
<span class="ident">test</span>(<span class="ident">_neg1_1i</span>, <span class="string">"-1 + i"</span>);
<span class="ident">test</span>(<span class="ident">_neg1_1i</span>, <span class="string">"-1+j"</span>);
<span class="ident">test</span>(<span class="ident">_neg1_1i</span>, <span class="string">"-1 + 1j"</span>);
<span class="ident">test</span>(<span class="ident">_neg1_1i</span>, <span class="string">"-1+1i"</span>);
<span class="ident">test</span>(<span class="ident">_neg1_1i</span>, <span class="string">"1i-1"</span>);
<span class="ident">test</span>(<span class="ident">_neg1_1i</span>, <span class="string">"j + -1"</span>);
<span class="ident">test</span>(<span class="ident">_05_05i</span>, <span class="string">"0.5 + 0.5i"</span>);
<span class="ident">test</span>(<span class="ident">_05_05i</span>, <span class="string">"0.5+0.5j"</span>);
<span class="ident">test</span>(<span class="ident">_05_05i</span>, <span class="string">"5e-1+0.5j"</span>);
<span class="ident">test</span>(<span class="ident">_05_05i</span>, <span class="string">"5E-1 + 0.5j"</span>);
<span class="ident">test</span>(<span class="ident">_05_05i</span>, <span class="string">"5E-1i + 0.5"</span>);
<span class="ident">test</span>(<span class="ident">_05_05i</span>, <span class="string">"0.05e+1j + 50E-2"</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_from_str_radix</span>() {
<span class="kw">fn</span> <span class="ident">test</span>(<span class="ident">z</span>: <span class="ident">Complex64</span>, <span class="ident">s</span>: <span class="kw-2">&</span><span class="ident">str</span>, <span class="ident">radix</span>: <span class="ident">u32</span>) {
<span class="kw">let</span> <span class="ident">res</span>: <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">Complex64</span>, <span class="op"><</span><span class="ident">Complex64</span> <span class="kw">as</span> <span class="ident">Num</span><span class="op">></span><span class="ident">::FromStrRadixErr</span><span class="op">></span>
<span class="op">=</span> <span class="ident">Num::from_str_radix</span>(<span class="ident">s</span>, <span class="ident">radix</span>);
<span class="macro">assert_eq!</span>(<span class="ident">res</span>.<span class="ident">unwrap</span>(), <span class="ident">z</span>)
}
<span class="ident">test</span>(<span class="ident">_4_2i</span>, <span class="string">"4+2i"</span>, <span class="number">10</span>);
<span class="ident">test</span>(<span class="ident">Complex::new</span>(<span class="number">15.0</span>, <span class="number">32.0</span>), <span class="string">"F+20i"</span>, <span class="number">16</span>);
<span class="ident">test</span>(<span class="ident">Complex::new</span>(<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="ident">test</span>(<span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">15.0</span>, <span class="op">-</span><span class="number">32.0</span>), <span class="string">"-F-20i"</span>, <span class="number">16</span>);
<span class="ident">test</span>(<span class="ident">Complex::new</span>(<span class="op">-</span><span class="number">15.0</span>, <span class="op">-</span><span class="number">32.0</span>), <span class="string">"-1111-100000i"</span>, <span class="number">2</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_from_str_fail</span>() {
<span class="kw">fn</span> <span class="ident">test</span>(<span class="ident">s</span>: <span class="kw-2">&</span><span class="ident">str</span>) {
<span class="kw">let</span> <span class="ident">complex</span>: <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">Complex64</span>, <span class="kw">_</span><span class="op">></span> <span class="op">=</span> <span class="ident">FromStr::from_str</span>(<span class="ident">s</span>);
<span class="macro">assert!</span>(<span class="ident">complex</span>.<span class="ident">is_err</span>());
}
<span class="ident">test</span>(<span class="string">"foo"</span>);
<span class="ident">test</span>(<span class="string">"6E"</span>);
<span class="ident">test</span>(<span class="string">"0 + 2.718"</span>);
<span class="ident">test</span>(<span class="string">"1 - -2i"</span>);
<span class="ident">test</span>(<span class="string">"314e-2ij"</span>);
<span class="ident">test</span>(<span class="string">"4.3j - i"</span>);
<span class="ident">test</span>(<span class="string">"1i - 2i"</span>);
<span class="ident">test</span>(<span class="string">"+ 1 - 3.0i"</span>);
}
}
</pre></div>
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