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</pre><pre class="rust ">
<span class="kw">use</span> <span class="ident">core</span>::<span class="ident">mem</span>;
<span class="kw">use</span> <span class="ident">core</span>::<span class="ident">ops</span>::<span class="ident">Neg</span>;
<span class="kw">use</span> <span class="ident">core</span>::<span class="ident">num</span>::<span class="ident">FpCategory</span>;
<span class="kw">use</span> <span class="ident">core</span>::<span class="ident">f32</span>;
<span class="kw">use</span> <span class="ident">core</span>::<span class="ident">f64</span>;
<span class="kw">use</span> {<span class="ident">Num</span>, <span class="ident">NumCast</span>, <span class="ident">ToPrimitive</span>};
<span class="doccomment">/// Generic trait for floating point numbers that works with `no_std`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This trait implements a subset of the `Float` trait.</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">FloatCore</span>: <span class="ident">Num</span> <span class="op">+</span> <span class="ident">NumCast</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="self">Self</span><span class="op">></span> <span class="op">+</span> <span class="ident">PartialOrd</span> <span class="op">+</span> <span class="ident">Copy</span> {
<span class="doccomment">/// Returns positive infinity.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T) {</span>
<span class="doccomment">/// assert!(T::infinity() == x);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY);</span>
<span class="doccomment">/// check(f64::INFINITY);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">infinity</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns negative infinity.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T) {</span>
<span class="doccomment">/// assert!(T::neg_infinity() == x);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::NEG_INFINITY);</span>
<span class="doccomment">/// check(f64::NEG_INFINITY);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">neg_infinity</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns NaN.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>() {</span>
<span class="doccomment">/// let n = T::nan();</span>
<span class="doccomment">/// assert!(n != n);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check::<f32>();</span>
<span class="doccomment">/// check::<f64>();</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">nan</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns `-0.0`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(n: T) {</span>
<span class="doccomment">/// let z = T::neg_zero();</span>
<span class="doccomment">/// assert!(z.is_zero());</span>
<span class="doccomment">/// assert!(T::one() / z == n);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::NEG_INFINITY);</span>
<span class="doccomment">/// check(f64::NEG_INFINITY);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">neg_zero</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the smallest finite value that this type can represent.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T) {</span>
<span class="doccomment">/// assert!(T::min_value() == x);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::MIN);</span>
<span class="doccomment">/// check(f64::MIN);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">min_value</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the smallest positive, normalized value that this type can represent.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T) {</span>
<span class="doccomment">/// assert!(T::min_positive_value() == x);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::MIN_POSITIVE);</span>
<span class="doccomment">/// check(f64::MIN_POSITIVE);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">min_positive_value</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns epsilon, a small positive value.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T) {</span>
<span class="doccomment">/// assert!(T::epsilon() == x);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::EPSILON);</span>
<span class="doccomment">/// check(f64::EPSILON);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">epsilon</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the largest finite value that this type can represent.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T) {</span>
<span class="doccomment">/// assert!(T::max_value() == x);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::MAX);</span>
<span class="doccomment">/// check(f64::MAX);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">max_value</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns `true` if the number is NaN.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, p: bool) {</span>
<span class="doccomment">/// assert!(x.is_nan() == p);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::NAN, true);</span>
<span class="doccomment">/// check(f32::INFINITY, false);</span>
<span class="doccomment">/// check(f64::NAN, true);</span>
<span class="doccomment">/// check(0.0f64, false);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_nan</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span> {
<span class="self">self</span> <span class="op">!=</span> <span class="self">self</span>
}
<span class="doccomment">/// Returns `true` if the number is infinite.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, p: bool) {</span>
<span class="doccomment">/// assert!(x.is_infinite() == p);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, true);</span>
<span class="doccomment">/// check(f32::NEG_INFINITY, true);</span>
<span class="doccomment">/// check(f32::NAN, false);</span>
<span class="doccomment">/// check(f64::INFINITY, true);</span>
<span class="doccomment">/// check(f64::NEG_INFINITY, true);</span>
<span class="doccomment">/// check(0.0f64, false);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_infinite</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span> {
<span class="self">self</span> <span class="op">==</span> <span class="self">Self</span>::<span class="ident">infinity</span>() <span class="op">||</span> <span class="self">self</span> <span class="op">==</span> <span class="self">Self</span>::<span class="ident">neg_infinity</span>()
}
<span class="doccomment">/// Returns `true` if the number is neither infinite or NaN.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, p: bool) {</span>
<span class="doccomment">/// assert!(x.is_finite() == p);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, false);</span>
<span class="doccomment">/// check(f32::MAX, true);</span>
<span class="doccomment">/// check(f64::NEG_INFINITY, false);</span>
<span class="doccomment">/// check(f64::MIN_POSITIVE, true);</span>
<span class="doccomment">/// check(f64::NAN, false);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_finite</span>(<span class="self">self</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">is_infinite</span>())
}
<span class="doccomment">/// Returns `true` if the number is neither zero, infinite, subnormal or NaN.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, p: bool) {</span>
<span class="doccomment">/// assert!(x.is_normal() == p);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, false);</span>
<span class="doccomment">/// check(f32::MAX, true);</span>
<span class="doccomment">/// check(f64::NEG_INFINITY, false);</span>
<span class="doccomment">/// check(f64::MIN_POSITIVE, true);</span>
<span class="doccomment">/// check(0.0f64, false);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_normal</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span> {
<span class="self">self</span>.<span class="ident">classify</span>() <span class="op">==</span> <span class="ident">FpCategory</span>::<span class="ident">Normal</span>
}
<span class="doccomment">/// Returns the floating point category of the number. If only one property</span>
<span class="doccomment">/// is going to be tested, it is generally faster to use the specific</span>
<span class="doccomment">/// predicate instead.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">/// use std::num::FpCategory;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, c: FpCategory) {</span>
<span class="doccomment">/// assert!(x.classify() == c);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, FpCategory::Infinite);</span>
<span class="doccomment">/// check(f32::MAX, FpCategory::Normal);</span>
<span class="doccomment">/// check(f64::NAN, FpCategory::Nan);</span>
<span class="doccomment">/// check(f64::MIN_POSITIVE, FpCategory::Normal);</span>
<span class="doccomment">/// check(f64::MIN_POSITIVE / 2.0, FpCategory::Subnormal);</span>
<span class="doccomment">/// check(0.0f64, FpCategory::Zero);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">classify</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">FpCategory</span>;
<span class="doccomment">/// Returns the largest integer less than or equal to a number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, y: T) {</span>
<span class="doccomment">/// assert!(x.floor() == y);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, f32::INFINITY);</span>
<span class="doccomment">/// check(0.9f32, 0.0);</span>
<span class="doccomment">/// check(1.0f32, 1.0);</span>
<span class="doccomment">/// check(1.1f32, 1.0);</span>
<span class="doccomment">/// check(-0.0f64, 0.0);</span>
<span class="doccomment">/// check(-0.9f64, -1.0);</span>
<span class="doccomment">/// check(-1.0f64, -1.0);</span>
<span class="doccomment">/// check(-1.1f64, -2.0);</span>
<span class="doccomment">/// check(f64::MIN, f64::MIN);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">floor</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">let</span> <span class="ident">f</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">fract</span>();
<span class="kw">if</span> <span class="ident">f</span>.<span class="ident">is_nan</span>() <span class="op">||</span> <span class="ident">f</span>.<span class="ident">is_zero</span>() {
<span class="self">self</span>
} <span class="kw">else</span> <span class="kw">if</span> <span class="self">self</span> <span class="op"><</span> <span class="self">Self</span>::<span class="ident">zero</span>() {
<span class="self">self</span> <span class="op">-</span> <span class="ident">f</span> <span class="op">-</span> <span class="self">Self</span>::<span class="ident">one</span>()
} <span class="kw">else</span> {
<span class="self">self</span> <span class="op">-</span> <span class="ident">f</span>
}
}
<span class="doccomment">/// Returns the smallest integer greater than or equal to a number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, y: T) {</span>
<span class="doccomment">/// assert!(x.ceil() == y);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, f32::INFINITY);</span>
<span class="doccomment">/// check(0.9f32, 1.0);</span>
<span class="doccomment">/// check(1.0f32, 1.0);</span>
<span class="doccomment">/// check(1.1f32, 2.0);</span>
<span class="doccomment">/// check(-0.0f64, 0.0);</span>
<span class="doccomment">/// check(-0.9f64, -0.0);</span>
<span class="doccomment">/// check(-1.0f64, -1.0);</span>
<span class="doccomment">/// check(-1.1f64, -1.0);</span>
<span class="doccomment">/// check(f64::MIN, f64::MIN);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">ceil</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">let</span> <span class="ident">f</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">fract</span>();
<span class="kw">if</span> <span class="ident">f</span>.<span class="ident">is_nan</span>() <span class="op">||</span> <span class="ident">f</span>.<span class="ident">is_zero</span>() {
<span class="self">self</span>
} <span class="kw">else</span> <span class="kw">if</span> <span class="self">self</span> <span class="op">></span> <span class="self">Self</span>::<span class="ident">zero</span>() {
<span class="self">self</span> <span class="op">-</span> <span class="ident">f</span> <span class="op">+</span> <span class="self">Self</span>::<span class="ident">one</span>()
} <span class="kw">else</span> {
<span class="self">self</span> <span class="op">-</span> <span class="ident">f</span>
}
}
<span class="doccomment">/// Returns the nearest integer to a number. Round half-way cases away from `0.0`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, y: T) {</span>
<span class="doccomment">/// assert!(x.round() == y);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, f32::INFINITY);</span>
<span class="doccomment">/// check(0.4f32, 0.0);</span>
<span class="doccomment">/// check(0.5f32, 1.0);</span>
<span class="doccomment">/// check(0.6f32, 1.0);</span>
<span class="doccomment">/// check(-0.4f64, 0.0);</span>
<span class="doccomment">/// check(-0.5f64, -1.0);</span>
<span class="doccomment">/// check(-0.6f64, -1.0);</span>
<span class="doccomment">/// check(f64::MIN, f64::MIN);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">round</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">let</span> <span class="ident">one</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">one</span>();
<span class="kw">let</span> <span class="ident">h</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">from</span>(<span class="number">0.5</span>).<span class="ident">expect</span>(<span class="string">"Unable to cast from 0.5"</span>);
<span class="kw">let</span> <span class="ident">f</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">fract</span>();
<span class="kw">if</span> <span class="ident">f</span>.<span class="ident">is_nan</span>() <span class="op">||</span> <span class="ident">f</span>.<span class="ident">is_zero</span>() {
<span class="self">self</span>
} <span class="kw">else</span> <span class="kw">if</span> <span class="self">self</span> <span class="op">></span> <span class="self">Self</span>::<span class="ident">zero</span>() {
<span class="kw">if</span> <span class="ident">f</span> <span class="op"><</span> <span class="ident">h</span> {
<span class="self">self</span> <span class="op">-</span> <span class="ident">f</span>
} <span class="kw">else</span> {
<span class="self">self</span> <span class="op">-</span> <span class="ident">f</span> <span class="op">+</span> <span class="ident">one</span>
}
} <span class="kw">else</span> {
<span class="kw">if</span> <span class="op">-</span><span class="ident">f</span> <span class="op"><</span> <span class="ident">h</span> {
<span class="self">self</span> <span class="op">-</span> <span class="ident">f</span>
} <span class="kw">else</span> {
<span class="self">self</span> <span class="op">-</span> <span class="ident">f</span> <span class="op">-</span> <span class="ident">one</span>
}
}
}
<span class="doccomment">/// Return the integer part of a number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, y: T) {</span>
<span class="doccomment">/// assert!(x.trunc() == y);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, f32::INFINITY);</span>
<span class="doccomment">/// check(0.9f32, 0.0);</span>
<span class="doccomment">/// check(1.0f32, 1.0);</span>
<span class="doccomment">/// check(1.1f32, 1.0);</span>
<span class="doccomment">/// check(-0.0f64, 0.0);</span>
<span class="doccomment">/// check(-0.9f64, -0.0);</span>
<span class="doccomment">/// check(-1.0f64, -1.0);</span>
<span class="doccomment">/// check(-1.1f64, -1.0);</span>
<span class="doccomment">/// check(f64::MIN, f64::MIN);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">trunc</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">let</span> <span class="ident">f</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">fract</span>();
<span class="kw">if</span> <span class="ident">f</span>.<span class="ident">is_nan</span>() {
<span class="self">self</span>
} <span class="kw">else</span> {
<span class="self">self</span> <span class="op">-</span> <span class="ident">f</span>
}
}
<span class="doccomment">/// Returns the fractional part of a number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, y: T) {</span>
<span class="doccomment">/// assert!(x.fract() == y);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::MAX, 0.0);</span>
<span class="doccomment">/// check(0.75f32, 0.75);</span>
<span class="doccomment">/// check(1.0f32, 0.0);</span>
<span class="doccomment">/// check(1.25f32, 0.25);</span>
<span class="doccomment">/// check(-0.0f64, 0.0);</span>
<span class="doccomment">/// check(-0.75f64, -0.75);</span>
<span class="doccomment">/// check(-1.0f64, 0.0);</span>
<span class="doccomment">/// check(-1.25f64, -0.25);</span>
<span class="doccomment">/// check(f64::MIN, 0.0);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">fract</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">is_zero</span>() {
<span class="self">Self</span>::<span class="ident">zero</span>()
} <span class="kw">else</span> {
<span class="self">self</span> <span class="op">%</span> <span class="self">Self</span>::<span class="ident">one</span>()
}
}
<span class="doccomment">/// Computes the absolute value of `self`. Returns `FloatCore::nan()` if the</span>
<span class="doccomment">/// number is `FloatCore::nan()`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, y: T) {</span>
<span class="doccomment">/// assert!(x.abs() == y);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, f32::INFINITY);</span>
<span class="doccomment">/// check(1.0f32, 1.0);</span>
<span class="doccomment">/// check(0.0f64, 0.0);</span>
<span class="doccomment">/// check(-0.0f64, 0.0);</span>
<span class="doccomment">/// check(-1.0f64, 1.0);</span>
<span class="doccomment">/// check(f64::MIN, f64::MAX);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">abs</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">is_sign_positive</span>() {
<span class="kw">return</span> <span class="self">self</span>;
}
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">is_sign_negative</span>() {
<span class="kw">return</span> <span class="op">-</span><span class="self">self</span>;
}
<span class="self">Self</span>::<span class="ident">nan</span>()
}
<span class="doccomment">/// Returns a number that represents the sign of `self`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// - `1.0` if the number is positive, `+0.0` or `FloatCore::infinity()`</span>
<span class="doccomment">/// - `-1.0` if the number is negative, `-0.0` or `FloatCore::neg_infinity()`</span>
<span class="doccomment">/// - `FloatCore::nan()` if the number is `FloatCore::nan()`</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, y: T) {</span>
<span class="doccomment">/// assert!(x.signum() == y);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, 1.0);</span>
<span class="doccomment">/// check(3.0f32, 1.0);</span>
<span class="doccomment">/// check(0.0f32, 1.0);</span>
<span class="doccomment">/// check(-0.0f64, -1.0);</span>
<span class="doccomment">/// check(-3.0f64, -1.0);</span>
<span class="doccomment">/// check(f64::MIN, -1.0);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">signum</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">is_nan</span>() {
<span class="self">Self</span>::<span class="ident">nan</span>()
} <span class="kw">else</span> <span class="kw">if</span> <span class="self">self</span>.<span class="ident">is_sign_negative</span>() {
<span class="op">-</span><span class="self">Self</span>::<span class="ident">one</span>()
} <span class="kw">else</span> {
<span class="self">Self</span>::<span class="ident">one</span>()
}
}
<span class="doccomment">/// Returns `true` if `self` is positive, including `+0.0` and</span>
<span class="doccomment">/// `FloatCore::infinity()`, and since Rust 1.20 also</span>
<span class="doccomment">/// `FloatCore::nan()`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, p: bool) {</span>
<span class="doccomment">/// assert!(x.is_sign_positive() == p);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, true);</span>
<span class="doccomment">/// check(f32::MAX, true);</span>
<span class="doccomment">/// check(0.0f32, true);</span>
<span class="doccomment">/// check(-0.0f64, false);</span>
<span class="doccomment">/// check(f64::NEG_INFINITY, false);</span>
<span class="doccomment">/// check(f64::MIN_POSITIVE, true);</span>
<span class="doccomment">/// check(-f64::NAN, false);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_sign_positive</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span> {
<span class="op">!</span><span class="self">self</span>.<span class="ident">is_sign_negative</span>()
}
<span class="doccomment">/// Returns `true` if `self` is negative, including `-0.0` and</span>
<span class="doccomment">/// `FloatCore::neg_infinity()`, and since Rust 1.20 also</span>
<span class="doccomment">/// `-FloatCore::nan()`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, p: bool) {</span>
<span class="doccomment">/// assert!(x.is_sign_negative() == p);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, false);</span>
<span class="doccomment">/// check(f32::MAX, false);</span>
<span class="doccomment">/// check(0.0f32, false);</span>
<span class="doccomment">/// check(-0.0f64, true);</span>
<span class="doccomment">/// check(f64::NEG_INFINITY, true);</span>
<span class="doccomment">/// check(f64::MIN_POSITIVE, false);</span>
<span class="doccomment">/// check(f64::NAN, false);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_sign_negative</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span> {
<span class="kw">let</span> (_, _, <span class="ident">sign</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">integer_decode</span>();
<span class="ident">sign</span> <span class="op"><</span> <span class="number">0</span>
}
<span class="doccomment">/// Returns the minimum of the two numbers.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// If one of the arguments is NaN, then the other argument is returned.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, y: T, min: T) {</span>
<span class="doccomment">/// assert!(x.min(y) == min);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(1.0f32, 2.0, 1.0);</span>
<span class="doccomment">/// check(f32::NAN, 2.0, 2.0);</span>
<span class="doccomment">/// check(1.0f64, -2.0, -2.0);</span>
<span class="doccomment">/// check(1.0f64, f64::NAN, 1.0);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">min</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">is_nan</span>() {
<span class="kw">return</span> <span class="ident">other</span>;
}
<span class="kw">if</span> <span class="ident">other</span>.<span class="ident">is_nan</span>() {
<span class="kw">return</span> <span class="self">self</span>;
}
<span class="kw">if</span> <span class="self">self</span> <span class="op"><</span> <span class="ident">other</span> { <span class="self">self</span> } <span class="kw">else</span> { <span class="ident">other</span> }
}
<span class="doccomment">/// Returns the maximum of the two numbers.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// If one of the arguments is NaN, then the other argument is returned.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, y: T, min: T) {</span>
<span class="doccomment">/// assert!(x.max(y) == min);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(1.0f32, 2.0, 2.0);</span>
<span class="doccomment">/// check(1.0f32, f32::NAN, 1.0);</span>
<span class="doccomment">/// check(-1.0f64, 2.0, 2.0);</span>
<span class="doccomment">/// check(-1.0f64, f64::NAN, -1.0);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">max</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">is_nan</span>() {
<span class="kw">return</span> <span class="ident">other</span>;
}
<span class="kw">if</span> <span class="ident">other</span>.<span class="ident">is_nan</span>() {
<span class="kw">return</span> <span class="self">self</span>;
}
<span class="kw">if</span> <span class="self">self</span> <span class="op">></span> <span class="ident">other</span> { <span class="self">self</span> } <span class="kw">else</span> { <span class="ident">other</span> }
}
<span class="doccomment">/// Returns the reciprocal (multiplicative inverse) of the number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, y: T) {</span>
<span class="doccomment">/// assert!(x.recip() == y);</span>
<span class="doccomment">/// assert!(y.recip() == x);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(f32::INFINITY, 0.0);</span>
<span class="doccomment">/// check(2.0f32, 0.5);</span>
<span class="doccomment">/// check(-0.25f64, -4.0);</span>
<span class="doccomment">/// check(-0.0f64, f64::NEG_INFINITY);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">recip</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="self">Self</span>::<span class="ident">one</span>() <span class="op">/</span> <span class="self">self</span>
}
<span class="doccomment">/// Raise a number to an integer power.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Using this function is generally faster than using `powf`</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, exp: i32, powi: T) {</span>
<span class="doccomment">/// assert!(x.powi(exp) == powi);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(9.0f32, 2, 81.0);</span>
<span class="doccomment">/// check(1.0f32, -2, 1.0);</span>
<span class="doccomment">/// check(10.0f64, 20, 1e20);</span>
<span class="doccomment">/// check(4.0f64, -2, 0.0625);</span>
<span class="doccomment">/// check(-1.0f64, std::i32::MIN, 1.0);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">powi</span>(<span class="kw-2">mut</span> <span class="self">self</span>, <span class="kw-2">mut</span> <span class="ident">exp</span>: <span class="ident">i32</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">if</span> <span class="ident">exp</span> <span class="op"><</span> <span class="number">0</span> {
<span class="ident">exp</span> <span class="op">=</span> <span class="ident">exp</span>.<span class="ident">wrapping_neg</span>();
<span class="self">self</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">recip</span>();
}
<span class="comment">// It should always be possible to convert a positive `i32` to a `usize`.</span>
<span class="comment">// Note, `i32::MIN` will wrap and still be negative, so we need to convert</span>
<span class="comment">// to `u32` without sign-extension before growing to `usize`.</span>
<span class="kw">super</span>::<span class="ident">pow</span>(<span class="self">self</span>, (<span class="ident">exp</span> <span class="kw">as</span> <span class="ident">u32</span>).<span class="ident">to_usize</span>().<span class="ident">unwrap</span>())
}
<span class="doccomment">/// Converts to degrees, assuming the number is in radians.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(rad: T, deg: T) {</span>
<span class="doccomment">/// assert!(rad.to_degrees() == deg);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(0.0f32, 0.0);</span>
<span class="doccomment">/// check(f32::consts::PI, 180.0);</span>
<span class="doccomment">/// check(f64::consts::FRAC_PI_4, 45.0);</span>
<span class="doccomment">/// check(f64::INFINITY, f64::INFINITY);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">to_degrees</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Converts to radians, assuming the number is in degrees.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(deg: T, rad: T) {</span>
<span class="doccomment">/// assert!(deg.to_radians() == rad);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(0.0f32, 0.0);</span>
<span class="doccomment">/// check(180.0, f32::consts::PI);</span>
<span class="doccomment">/// check(45.0, f64::consts::FRAC_PI_4);</span>
<span class="doccomment">/// check(f64::INFINITY, f64::INFINITY);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">to_radians</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the mantissa, base 2 exponent, and sign as integers, respectively.</span>
<span class="doccomment">/// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::float::FloatCore;</span>
<span class="doccomment">/// use std::{f32, f64};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// fn check<T: FloatCore>(x: T, m: u64, e: i16, s:i8) {</span>
<span class="doccomment">/// let (mantissa, exponent, sign) = x.integer_decode();</span>
<span class="doccomment">/// assert_eq!(mantissa, m);</span>
<span class="doccomment">/// assert_eq!(exponent, e);</span>
<span class="doccomment">/// assert_eq!(sign, s);</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// check(2.0f32, 1 << 23, -22, 1);</span>
<span class="doccomment">/// check(-2.0f32, 1 << 23, -22, -1);</span>
<span class="doccomment">/// check(f32::INFINITY, 1 << 23, 105, 1);</span>
<span class="doccomment">/// check(f64::NEG_INFINITY, 1 << 52, 972, -1);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">integer_decode</span>(<span class="self">self</span>) <span class="op">-></span> (<span class="ident">u64</span>, <span class="ident">i16</span>, <span class="ident">i8</span>);
}
<span class="kw">impl</span> <span class="ident">FloatCore</span> <span class="kw">for</span> <span class="ident">f32</span> {
<span class="macro">constant</span><span class="macro">!</span> {
<span class="ident">infinity</span>() <span class="op">-></span> <span class="ident">f32</span>::<span class="ident">INFINITY</span>;
<span class="ident">neg_infinity</span>() <span class="op">-></span> <span class="ident">f32</span>::<span class="ident">NEG_INFINITY</span>;
<span class="ident">nan</span>() <span class="op">-></span> <span class="ident">f32</span>::<span class="ident">NAN</span>;
<span class="ident">neg_zero</span>() <span class="op">-></span> <span class="op">-</span><span class="number">0.0</span>;
<span class="ident">min_value</span>() <span class="op">-></span> <span class="ident">f32</span>::<span class="ident">MIN</span>;
<span class="ident">min_positive_value</span>() <span class="op">-></span> <span class="ident">f32</span>::<span class="ident">MIN_POSITIVE</span>;
<span class="ident">epsilon</span>() <span class="op">-></span> <span class="ident">f32</span>::<span class="ident">EPSILON</span>;
<span class="ident">max_value</span>() <span class="op">-></span> <span class="ident">f32</span>::<span class="ident">MAX</span>;
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">integer_decode</span>(<span class="self">self</span>) <span class="op">-></span> (<span class="ident">u64</span>, <span class="ident">i16</span>, <span class="ident">i8</span>) {
<span class="ident">integer_decode_f32</span>(<span class="self">self</span>)
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">not</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>))]</span>
<span class="kw">fn</span> <span class="ident">classify</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">FpCategory</span> {
<span class="kw">const</span> <span class="ident">EXP_MASK</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="number">0x7f800000</span>;
<span class="kw">const</span> <span class="ident">MAN_MASK</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="number">0x007fffff</span>;
<span class="kw">let</span> <span class="ident">bits</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">mem</span>::<span class="ident">transmute</span>(<span class="self">self</span>) };
<span class="kw">match</span> (<span class="ident">bits</span> <span class="op">&</span> <span class="ident">MAN_MASK</span>, <span class="ident">bits</span> <span class="op">&</span> <span class="ident">EXP_MASK</span>) {
(<span class="number">0</span>, <span class="number">0</span>) <span class="op">=></span> <span class="ident">FpCategory</span>::<span class="ident">Zero</span>,
(_, <span class="number">0</span>) <span class="op">=></span> <span class="ident">FpCategory</span>::<span class="ident">Subnormal</span>,
(<span class="number">0</span>, <span class="ident">EXP_MASK</span>) <span class="op">=></span> <span class="ident">FpCategory</span>::<span class="ident">Infinite</span>,
(_, <span class="ident">EXP_MASK</span>) <span class="op">=></span> <span class="ident">FpCategory</span>::<span class="ident">Nan</span>,
_ <span class="op">=></span> <span class="ident">FpCategory</span>::<span class="ident">Normal</span>,
}
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">not</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>))]</span>
<span class="kw">fn</span> <span class="ident">to_degrees</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="self">self</span> <span class="op">*</span> (<span class="number">180.0</span> <span class="op">/</span> <span class="ident">f32</span>::<span class="ident">consts</span>::<span class="ident">PI</span>)
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">not</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>))]</span>
<span class="kw">fn</span> <span class="ident">to_radians</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="self">self</span> <span class="op">*</span> (<span class="ident">f32</span>::<span class="ident">consts</span>::<span class="ident">PI</span> <span class="op">/</span> <span class="number">180.0</span>)
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>)]</span>
<span class="macro">forward</span><span class="macro">!</span> {
<span class="self">Self</span>::<span class="ident">is_nan</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_infinite</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_finite</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_normal</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">classify</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">FpCategory</span>;
<span class="self">Self</span>::<span class="ident">floor</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">ceil</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">round</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">trunc</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">fract</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">abs</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">signum</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">is_sign_positive</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_sign_negative</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">min</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">max</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">recip</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">powi</span>(<span class="self">self</span>, <span class="ident">n</span>: <span class="ident">i32</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">to_degrees</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">to_radians</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
}
}
<span class="kw">impl</span> <span class="ident">FloatCore</span> <span class="kw">for</span> <span class="ident">f64</span> {
<span class="macro">constant</span><span class="macro">!</span> {
<span class="ident">infinity</span>() <span class="op">-></span> <span class="ident">f64</span>::<span class="ident">INFINITY</span>;
<span class="ident">neg_infinity</span>() <span class="op">-></span> <span class="ident">f64</span>::<span class="ident">NEG_INFINITY</span>;
<span class="ident">nan</span>() <span class="op">-></span> <span class="ident">f64</span>::<span class="ident">NAN</span>;
<span class="ident">neg_zero</span>() <span class="op">-></span> <span class="op">-</span><span class="number">0.0</span>;
<span class="ident">min_value</span>() <span class="op">-></span> <span class="ident">f64</span>::<span class="ident">MIN</span>;
<span class="ident">min_positive_value</span>() <span class="op">-></span> <span class="ident">f64</span>::<span class="ident">MIN_POSITIVE</span>;
<span class="ident">epsilon</span>() <span class="op">-></span> <span class="ident">f64</span>::<span class="ident">EPSILON</span>;
<span class="ident">max_value</span>() <span class="op">-></span> <span class="ident">f64</span>::<span class="ident">MAX</span>;
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">integer_decode</span>(<span class="self">self</span>) <span class="op">-></span> (<span class="ident">u64</span>, <span class="ident">i16</span>, <span class="ident">i8</span>) {
<span class="ident">integer_decode_f64</span>(<span class="self">self</span>)
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">not</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>))]</span>
<span class="kw">fn</span> <span class="ident">classify</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">FpCategory</span> {
<span class="kw">const</span> <span class="ident">EXP_MASK</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="number">0x7ff0000000000000</span>;
<span class="kw">const</span> <span class="ident">MAN_MASK</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="number">0x000fffffffffffff</span>;
<span class="kw">let</span> <span class="ident">bits</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">mem</span>::<span class="ident">transmute</span>(<span class="self">self</span>) };
<span class="kw">match</span> (<span class="ident">bits</span> <span class="op">&</span> <span class="ident">MAN_MASK</span>, <span class="ident">bits</span> <span class="op">&</span> <span class="ident">EXP_MASK</span>) {
(<span class="number">0</span>, <span class="number">0</span>) <span class="op">=></span> <span class="ident">FpCategory</span>::<span class="ident">Zero</span>,
(_, <span class="number">0</span>) <span class="op">=></span> <span class="ident">FpCategory</span>::<span class="ident">Subnormal</span>,
(<span class="number">0</span>, <span class="ident">EXP_MASK</span>) <span class="op">=></span> <span class="ident">FpCategory</span>::<span class="ident">Infinite</span>,
(_, <span class="ident">EXP_MASK</span>) <span class="op">=></span> <span class="ident">FpCategory</span>::<span class="ident">Nan</span>,
_ <span class="op">=></span> <span class="ident">FpCategory</span>::<span class="ident">Normal</span>,
}
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">not</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>))]</span>
<span class="kw">fn</span> <span class="ident">to_degrees</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="self">self</span> <span class="op">*</span> (<span class="number">180.0</span> <span class="op">/</span> <span class="ident">f64</span>::<span class="ident">consts</span>::<span class="ident">PI</span>)
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">not</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>))]</span>
<span class="kw">fn</span> <span class="ident">to_radians</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="self">self</span> <span class="op">*</span> (<span class="ident">f64</span>::<span class="ident">consts</span>::<span class="ident">PI</span> <span class="op">/</span> <span class="number">180.0</span>)
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>)]</span>
<span class="macro">forward</span><span class="macro">!</span> {
<span class="self">Self</span>::<span class="ident">is_nan</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_infinite</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_finite</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_normal</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">classify</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">FpCategory</span>;
<span class="self">Self</span>::<span class="ident">floor</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">ceil</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">round</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">trunc</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">fract</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">abs</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">signum</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">is_sign_positive</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_sign_negative</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">min</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">max</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">recip</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">powi</span>(<span class="self">self</span>, <span class="ident">n</span>: <span class="ident">i32</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">to_degrees</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">to_radians</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
}
}
<span class="comment">// FIXME: these doctests aren't actually helpful, because they're using and</span>
<span class="comment">// testing the inherent methods directly, not going through `Float`.</span>
<span class="doccomment">/// Generic trait for floating point numbers</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This trait is only available with the `std` feature.</span>
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>)]</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">Float</span>
: <span class="ident">Num</span>
<span class="op">+</span> <span class="ident">Copy</span>
<span class="op">+</span> <span class="ident">NumCast</span>
<span class="op">+</span> <span class="ident">PartialOrd</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="self">Self</span><span class="op">></span>
{
<span class="doccomment">/// Returns the `NaN` value.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let nan: f32 = Float::nan();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(nan.is_nan());</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">nan</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the infinite value.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f32;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let infinity: f32 = Float::infinity();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(infinity.is_infinite());</span>
<span class="doccomment">/// assert!(!infinity.is_finite());</span>
<span class="doccomment">/// assert!(infinity > f32::MAX);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">infinity</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the negative infinite value.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f32;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let neg_infinity: f32 = Float::neg_infinity();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(neg_infinity.is_infinite());</span>
<span class="doccomment">/// assert!(!neg_infinity.is_finite());</span>
<span class="doccomment">/// assert!(neg_infinity < f32::MIN);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">neg_infinity</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns `-0.0`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::{Zero, Float};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let inf: f32 = Float::infinity();</span>
<span class="doccomment">/// let zero: f32 = Zero::zero();</span>
<span class="doccomment">/// let neg_zero: f32 = Float::neg_zero();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(zero, neg_zero);</span>
<span class="doccomment">/// assert_eq!(7.0f32/inf, zero);</span>
<span class="doccomment">/// assert_eq!(zero * 10.0, zero);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">neg_zero</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the smallest finite value that this type can represent.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x: f64 = Float::min_value();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(x, f64::MIN);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">min_value</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the smallest positive, normalized value that this type can represent.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x: f64 = Float::min_positive_value();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(x, f64::MIN_POSITIVE);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">min_positive_value</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns epsilon, a small positive value.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x: f64 = Float::epsilon();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(x, f64::EPSILON);</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Panics</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The default implementation will panic if `f32::EPSILON` cannot</span>
<span class="doccomment">/// be cast to `Self`.</span>
<span class="kw">fn</span> <span class="ident">epsilon</span>() <span class="op">-></span> <span class="self">Self</span> {
<span class="self">Self</span>::<span class="ident">from</span>(<span class="ident">f32</span>::<span class="ident">EPSILON</span>).<span class="ident">expect</span>(<span class="string">"Unable to cast from f32::EPSILON"</span>)
}
<span class="doccomment">/// Returns the largest finite value that this type can represent.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x: f64 = Float::max_value();</span>
<span class="doccomment">/// assert_eq!(x, f64::MAX);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">max_value</span>() <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns `true` if this value is `NaN` and false otherwise.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let nan = f64::NAN;</span>
<span class="doccomment">/// let f = 7.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(nan.is_nan());</span>
<span class="doccomment">/// assert!(!f.is_nan());</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">is_nan</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="doccomment">/// Returns `true` if this value is positive infinity or negative infinity and</span>
<span class="doccomment">/// false otherwise.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f32;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 7.0f32;</span>
<span class="doccomment">/// let inf: f32 = Float::infinity();</span>
<span class="doccomment">/// let neg_inf: f32 = Float::neg_infinity();</span>
<span class="doccomment">/// let nan: f32 = f32::NAN;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(!f.is_infinite());</span>
<span class="doccomment">/// assert!(!nan.is_infinite());</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(inf.is_infinite());</span>
<span class="doccomment">/// assert!(neg_inf.is_infinite());</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">is_infinite</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="doccomment">/// Returns `true` if this number is neither infinite nor `NaN`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f32;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 7.0f32;</span>
<span class="doccomment">/// let inf: f32 = Float::infinity();</span>
<span class="doccomment">/// let neg_inf: f32 = Float::neg_infinity();</span>
<span class="doccomment">/// let nan: f32 = f32::NAN;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(f.is_finite());</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(!nan.is_finite());</span>
<span class="doccomment">/// assert!(!inf.is_finite());</span>
<span class="doccomment">/// assert!(!neg_inf.is_finite());</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">is_finite</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="doccomment">/// Returns `true` if the number is neither zero, infinite,</span>
<span class="doccomment">/// [subnormal][subnormal], or `NaN`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f32;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32</span>
<span class="doccomment">/// let max = f32::MAX;</span>
<span class="doccomment">/// let lower_than_min = 1.0e-40_f32;</span>
<span class="doccomment">/// let zero = 0.0f32;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(min.is_normal());</span>
<span class="doccomment">/// assert!(max.is_normal());</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(!zero.is_normal());</span>
<span class="doccomment">/// assert!(!f32::NAN.is_normal());</span>
<span class="doccomment">/// assert!(!f32::INFINITY.is_normal());</span>
<span class="doccomment">/// // Values between `0` and `min` are Subnormal.</span>
<span class="doccomment">/// assert!(!lower_than_min.is_normal());</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number</span>
<span class="kw">fn</span> <span class="ident">is_normal</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="doccomment">/// Returns the floating point category of the number. If only one property</span>
<span class="doccomment">/// is going to be tested, it is generally faster to use the specific</span>
<span class="doccomment">/// predicate instead.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::num::FpCategory;</span>
<span class="doccomment">/// use std::f32;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let num = 12.4f32;</span>
<span class="doccomment">/// let inf = f32::INFINITY;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(num.classify(), FpCategory::Normal);</span>
<span class="doccomment">/// assert_eq!(inf.classify(), FpCategory::Infinite);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">classify</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">FpCategory</span>;
<span class="doccomment">/// Returns the largest integer less than or equal to a number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 3.99;</span>
<span class="doccomment">/// let g = 3.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(f.floor(), 3.0);</span>
<span class="doccomment">/// assert_eq!(g.floor(), 3.0);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">floor</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the smallest integer greater than or equal to a number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 3.01;</span>
<span class="doccomment">/// let g = 4.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(f.ceil(), 4.0);</span>
<span class="doccomment">/// assert_eq!(g.ceil(), 4.0);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">ceil</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the nearest integer to a number. Round half-way cases away from</span>
<span class="doccomment">/// `0.0`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 3.3;</span>
<span class="doccomment">/// let g = -3.3;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(f.round(), 3.0);</span>
<span class="doccomment">/// assert_eq!(g.round(), -3.0);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">round</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Return the integer part of a number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 3.3;</span>
<span class="doccomment">/// let g = -3.7;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(f.trunc(), 3.0);</span>
<span class="doccomment">/// assert_eq!(g.trunc(), -3.0);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">trunc</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the fractional part of a number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 3.5;</span>
<span class="doccomment">/// let y = -3.5;</span>
<span class="doccomment">/// let abs_difference_x = (x.fract() - 0.5).abs();</span>
<span class="doccomment">/// let abs_difference_y = (y.fract() - (-0.5)).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference_x < 1e-10);</span>
<span class="doccomment">/// assert!(abs_difference_y < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">fract</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Computes the absolute value of `self`. Returns `Float::nan()` if the</span>
<span class="doccomment">/// number is `Float::nan()`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 3.5;</span>
<span class="doccomment">/// let y = -3.5;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference_x = (x.abs() - x).abs();</span>
<span class="doccomment">/// let abs_difference_y = (y.abs() - (-y)).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference_x < 1e-10);</span>
<span class="doccomment">/// assert!(abs_difference_y < 1e-10);</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(f64::NAN.abs().is_nan());</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">abs</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns a number that represents the sign of `self`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`</span>
<span class="doccomment">/// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`</span>
<span class="doccomment">/// - `Float::nan()` if the number is `Float::nan()`</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 3.5;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(f.signum(), 1.0);</span>
<span class="doccomment">/// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(f64::NAN.signum().is_nan());</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">signum</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns `true` if `self` is positive, including `+0.0`,</span>
<span class="doccomment">/// `Float::infinity()`, and since Rust 1.20 also `Float::nan()`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let neg_nan: f64 = -f64::NAN;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 7.0;</span>
<span class="doccomment">/// let g = -7.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(f.is_sign_positive());</span>
<span class="doccomment">/// assert!(!g.is_sign_positive());</span>
<span class="doccomment">/// assert!(!neg_nan.is_sign_positive());</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">is_sign_positive</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="doccomment">/// Returns `true` if `self` is negative, including `-0.0`,</span>
<span class="doccomment">/// `Float::neg_infinity()`, and since Rust 1.20 also `-Float::nan()`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let nan: f64 = f64::NAN;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 7.0;</span>
<span class="doccomment">/// let g = -7.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(!f.is_sign_negative());</span>
<span class="doccomment">/// assert!(g.is_sign_negative());</span>
<span class="doccomment">/// assert!(!nan.is_sign_negative());</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">is_sign_negative</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="doccomment">/// Fused multiply-add. Computes `(self * a) + b` with only one rounding</span>
<span class="doccomment">/// error. This produces a more accurate result with better performance than</span>
<span class="doccomment">/// a separate multiplication operation followed by an add.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let m = 10.0;</span>
<span class="doccomment">/// let x = 4.0;</span>
<span class="doccomment">/// let b = 60.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // 100.0</span>
<span class="doccomment">/// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">mul_add</span>(<span class="self">self</span>, <span class="ident">a</span>: <span class="self">Self</span>, <span class="ident">b</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Take the reciprocal (inverse) of a number, `1/x`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 2.0;</span>
<span class="doccomment">/// let abs_difference = (x.recip() - (1.0/x)).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">recip</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Raise a number to an integer power.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Using this function is generally faster than using `powf`</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 2.0;</span>
<span class="doccomment">/// let abs_difference = (x.powi(2) - x*x).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">powi</span>(<span class="self">self</span>, <span class="ident">n</span>: <span class="ident">i32</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Raise a number to a floating point power.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 2.0;</span>
<span class="doccomment">/// let abs_difference = (x.powf(2.0) - x*x).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">powf</span>(<span class="self">self</span>, <span class="ident">n</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Take the square root of a number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Returns NaN if `self` is a negative number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let positive = 4.0;</span>
<span class="doccomment">/// let negative = -4.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference = (positive.sqrt() - 2.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// assert!(negative.sqrt().is_nan());</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">sqrt</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns `e^(self)`, (the exponential function).</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let one = 1.0;</span>
<span class="doccomment">/// // e^1</span>
<span class="doccomment">/// let e = one.exp();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // ln(e) - 1 == 0</span>
<span class="doccomment">/// let abs_difference = (e.ln() - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">exp</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns `2^(self)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 2.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // 2^2 - 4 == 0</span>
<span class="doccomment">/// let abs_difference = (f.exp2() - 4.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">exp2</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the natural logarithm of the number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let one = 1.0;</span>
<span class="doccomment">/// // e^1</span>
<span class="doccomment">/// let e = one.exp();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // ln(e) - 1 == 0</span>
<span class="doccomment">/// let abs_difference = (e.ln() - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">ln</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the logarithm of the number with respect to an arbitrary base.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let ten = 10.0;</span>
<span class="doccomment">/// let two = 2.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // log10(10) - 1 == 0</span>
<span class="doccomment">/// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // log2(2) - 1 == 0</span>
<span class="doccomment">/// let abs_difference_2 = (two.log(2.0) - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference_10 < 1e-10);</span>
<span class="doccomment">/// assert!(abs_difference_2 < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">log</span>(<span class="self">self</span>, <span class="ident">base</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the base 2 logarithm of the number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let two = 2.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // log2(2) - 1 == 0</span>
<span class="doccomment">/// let abs_difference = (two.log2() - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">log2</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the base 10 logarithm of the number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let ten = 10.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // log10(10) - 1 == 0</span>
<span class="doccomment">/// let abs_difference = (ten.log10() - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">log10</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Converts radians to degrees.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use std::f64::consts;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let angle = consts::PI;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference = (angle.to_degrees() - 180.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">to_degrees</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">let</span> <span class="ident">halfpi</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">zero</span>().<span class="ident">acos</span>();
<span class="kw">let</span> <span class="ident">ninety</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">from</span>(<span class="number">90u8</span>).<span class="ident">unwrap</span>();
<span class="self">self</span> <span class="op">*</span> <span class="ident">ninety</span> <span class="op">/</span> <span class="ident">halfpi</span>
}
<span class="doccomment">/// Converts degrees to radians.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use std::f64::consts;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let angle = 180.0_f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference = (angle.to_radians() - consts::PI).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">to_radians</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="kw">let</span> <span class="ident">halfpi</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">zero</span>().<span class="ident">acos</span>();
<span class="kw">let</span> <span class="ident">ninety</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">from</span>(<span class="number">90u8</span>).<span class="ident">unwrap</span>();
<span class="self">self</span> <span class="op">*</span> <span class="ident">halfpi</span> <span class="op">/</span> <span class="ident">ninety</span>
}
<span class="doccomment">/// Returns the maximum of the two numbers.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 1.0;</span>
<span class="doccomment">/// let y = 2.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(x.max(y), y);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">max</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the minimum of the two numbers.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 1.0;</span>
<span class="doccomment">/// let y = 2.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(x.min(y), x);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">min</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// The positive difference of two numbers.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * If `self <= other`: `0:0`</span>
<span class="doccomment">/// * Else: `self - other`</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 3.0;</span>
<span class="doccomment">/// let y = -3.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();</span>
<span class="doccomment">/// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference_x < 1e-10);</span>
<span class="doccomment">/// assert!(abs_difference_y < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">abs_sub</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Take the cubic root of a number.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 8.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // x^(1/3) - 2 == 0</span>
<span class="doccomment">/// let abs_difference = (x.cbrt() - 2.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">cbrt</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Calculate the length of the hypotenuse of a right-angle triangle given</span>
<span class="doccomment">/// legs of length `x` and `y`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 2.0;</span>
<span class="doccomment">/// let y = 3.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // sqrt(x^2 + y^2)</span>
<span class="doccomment">/// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">hypot</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Computes the sine of a number (in radians).</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = f64::consts::PI/2.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference = (x.sin() - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">sin</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Computes the cosine of a number (in radians).</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 2.0*f64::consts::PI;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference = (x.cos() - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">cos</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Computes the tangent of a number (in radians).</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = f64::consts::PI/4.0;</span>
<span class="doccomment">/// let abs_difference = (x.tan() - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-14);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">tan</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Computes the arcsine of a number. Return value is in radians in</span>
<span class="doccomment">/// the range [-pi/2, pi/2] or NaN if the number is outside the range</span>
<span class="doccomment">/// [-1, 1].</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = f64::consts::PI / 2.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // asin(sin(pi/2))</span>
<span class="doccomment">/// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">asin</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Computes the arccosine of a number. Return value is in radians in</span>
<span class="doccomment">/// the range [0, pi] or NaN if the number is outside the range</span>
<span class="doccomment">/// [-1, 1].</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = f64::consts::PI / 4.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // acos(cos(pi/4))</span>
<span class="doccomment">/// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">acos</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Computes the arctangent of a number. Return value is in radians in the</span>
<span class="doccomment">/// range [-pi/2, pi/2];</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = 1.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // atan(tan(1))</span>
<span class="doccomment">/// let abs_difference = (f.tan().atan() - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">atan</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * `x = 0`, `y = 0`: `0`</span>
<span class="doccomment">/// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`</span>
<span class="doccomment">/// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`</span>
<span class="doccomment">/// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let pi = f64::consts::PI;</span>
<span class="doccomment">/// // All angles from horizontal right (+x)</span>
<span class="doccomment">/// // 45 deg counter-clockwise</span>
<span class="doccomment">/// let x1 = 3.0;</span>
<span class="doccomment">/// let y1 = -3.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // 135 deg clockwise</span>
<span class="doccomment">/// let x2 = -3.0;</span>
<span class="doccomment">/// let y2 = 3.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();</span>
<span class="doccomment">/// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference_1 < 1e-10);</span>
<span class="doccomment">/// assert!(abs_difference_2 < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">atan2</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Simultaneously computes the sine and cosine of the number, `x`. Returns</span>
<span class="doccomment">/// `(sin(x), cos(x))`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = f64::consts::PI/4.0;</span>
<span class="doccomment">/// let f = x.sin_cos();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference_0 = (f.0 - x.sin()).abs();</span>
<span class="doccomment">/// let abs_difference_1 = (f.1 - x.cos()).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference_0 < 1e-10);</span>
<span class="doccomment">/// assert!(abs_difference_0 < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">sin_cos</span>(<span class="self">self</span>) <span class="op">-></span> (<span class="self">Self</span>, <span class="self">Self</span>);
<span class="doccomment">/// Returns `e^(self) - 1` in a way that is accurate even if the</span>
<span class="doccomment">/// number is close to zero.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 7.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // e^(ln(7)) - 1</span>
<span class="doccomment">/// let abs_difference = (x.ln().exp_m1() - 6.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">exp_m1</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns `ln(1+n)` (natural logarithm) more accurately than if</span>
<span class="doccomment">/// the operations were performed separately.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = f64::consts::E - 1.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // ln(1 + (e - 1)) == ln(e) == 1</span>
<span class="doccomment">/// let abs_difference = (x.ln_1p() - 1.0).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">ln_1p</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Hyperbolic sine function.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let e = f64::consts::E;</span>
<span class="doccomment">/// let x = 1.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = x.sinh();</span>
<span class="doccomment">/// // Solving sinh() at 1 gives `(e^2-1)/(2e)`</span>
<span class="doccomment">/// let g = (e*e - 1.0)/(2.0*e);</span>
<span class="doccomment">/// let abs_difference = (f - g).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">sinh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Hyperbolic cosine function.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let e = f64::consts::E;</span>
<span class="doccomment">/// let x = 1.0;</span>
<span class="doccomment">/// let f = x.cosh();</span>
<span class="doccomment">/// // Solving cosh() at 1 gives this result</span>
<span class="doccomment">/// let g = (e*e + 1.0)/(2.0*e);</span>
<span class="doccomment">/// let abs_difference = (f - g).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // Same result</span>
<span class="doccomment">/// assert!(abs_difference < 1.0e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">cosh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Hyperbolic tangent function.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let e = f64::consts::E;</span>
<span class="doccomment">/// let x = 1.0;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let f = x.tanh();</span>
<span class="doccomment">/// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`</span>
<span class="doccomment">/// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));</span>
<span class="doccomment">/// let abs_difference = (f - g).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1.0e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">tanh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Inverse hyperbolic sine function.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 1.0;</span>
<span class="doccomment">/// let f = x.sinh().asinh();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference = (f - x).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1.0e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">asinh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Inverse hyperbolic cosine function.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let x = 1.0;</span>
<span class="doccomment">/// let f = x.cosh().acosh();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference = (f - x).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1.0e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">acosh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Inverse hyperbolic tangent function.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">/// use std::f64;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let e = f64::consts::E;</span>
<span class="doccomment">/// let f = e.tanh().atanh();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let abs_difference = (f - e).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1.0e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">atanh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Returns the mantissa, base 2 exponent, and sign as integers, respectively.</span>
<span class="doccomment">/// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use num_traits::Float;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let num = 2.0f32;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // (8388608, -22, 1)</span>
<span class="doccomment">/// let (mantissa, exponent, sign) = Float::integer_decode(num);</span>
<span class="doccomment">/// let sign_f = sign as f32;</span>
<span class="doccomment">/// let mantissa_f = mantissa as f32;</span>
<span class="doccomment">/// let exponent_f = num.powf(exponent as f32);</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // 1 * 8388608 * 2^(-22) == 2</span>
<span class="doccomment">/// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(abs_difference < 1e-10);</span>
<span class="doccomment">/// ```</span>
<span class="kw">fn</span> <span class="ident">integer_decode</span>(<span class="self">self</span>) <span class="op">-></span> (<span class="ident">u64</span>, <span class="ident">i16</span>, <span class="ident">i8</span>);
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>)]</span>
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">float_impl</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>:<span class="ident">ident</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">decode</span>:<span class="ident">ident</span>) <span class="op">=></span> (
<span class="kw">impl</span> <span class="ident">Float</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span> {
<span class="macro">constant</span><span class="macro">!</span> {
<span class="ident">nan</span>() <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>::<span class="ident">NAN</span>;
<span class="ident">infinity</span>() <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>::<span class="ident">INFINITY</span>;
<span class="ident">neg_infinity</span>() <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>::<span class="ident">NEG_INFINITY</span>;
<span class="ident">neg_zero</span>() <span class="op">-></span> <span class="op">-</span><span class="number">0.0</span>;
<span class="ident">min_value</span>() <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>::<span class="ident">MIN</span>;
<span class="ident">min_positive_value</span>() <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>::<span class="ident">MIN_POSITIVE</span>;
<span class="ident">epsilon</span>() <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>::<span class="ident">EPSILON</span>;
<span class="ident">max_value</span>() <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>::<span class="ident">MAX</span>;
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="attribute">#[<span class="ident">allow</span>(<span class="ident">deprecated</span>)]</span>
<span class="kw">fn</span> <span class="ident">abs_sub</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span><span class="op">></span>::<span class="ident">abs_sub</span>(<span class="self">self</span>, <span class="ident">other</span>)
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">integer_decode</span>(<span class="self">self</span>) <span class="op">-></span> (<span class="ident">u64</span>, <span class="ident">i16</span>, <span class="ident">i8</span>) {
<span class="macro-nonterminal">$</span><span class="macro-nonterminal">decode</span>(<span class="self">self</span>)
}
<span class="macro">forward</span><span class="macro">!</span> {
<span class="self">Self</span>::<span class="ident">is_nan</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_infinite</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_finite</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_normal</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">classify</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">FpCategory</span>;
<span class="self">Self</span>::<span class="ident">floor</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">ceil</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">round</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">trunc</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">fract</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">abs</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">signum</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">is_sign_positive</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">is_sign_negative</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span>;
<span class="self">Self</span>::<span class="ident">mul_add</span>(<span class="self">self</span>, <span class="ident">a</span>: <span class="self">Self</span>, <span class="ident">b</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">recip</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">powi</span>(<span class="self">self</span>, <span class="ident">n</span>: <span class="ident">i32</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">powf</span>(<span class="self">self</span>, <span class="ident">n</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">sqrt</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">exp</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">exp2</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">ln</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">log</span>(<span class="self">self</span>, <span class="ident">base</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">log2</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">log10</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">to_degrees</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">to_radians</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">max</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">min</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">cbrt</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">hypot</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">sin</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">cos</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">tan</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">asin</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">acos</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">atan</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">atan2</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">sin_cos</span>(<span class="self">self</span>) <span class="op">-></span> (<span class="self">Self</span>, <span class="self">Self</span>);
<span class="self">Self</span>::<span class="ident">exp_m1</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">ln_1p</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">sinh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">cosh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">tanh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">asinh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">acosh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="self">Self</span>::<span class="ident">atanh</span>(<span class="self">self</span>) <span class="op">-></span> <span class="self">Self</span>;
}
}
)
}
<span class="kw">fn</span> <span class="ident">integer_decode_f32</span>(<span class="ident">f</span>: <span class="ident">f32</span>) <span class="op">-></span> (<span class="ident">u64</span>, <span class="ident">i16</span>, <span class="ident">i8</span>) {
<span class="kw">let</span> <span class="ident">bits</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">mem</span>::<span class="ident">transmute</span>(<span class="ident">f</span>) };
<span class="kw">let</span> <span class="ident">sign</span>: <span class="ident">i8</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">bits</span> <span class="op">>></span> <span class="number">31</span> <span class="op">==</span> <span class="number">0</span> {
<span class="number">1</span>
} <span class="kw">else</span> {
<span class="op">-</span><span class="number">1</span>
};
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">exponent</span>: <span class="ident">i16</span> <span class="op">=</span> ((<span class="ident">bits</span> <span class="op">>></span> <span class="number">23</span>) <span class="op">&</span> <span class="number">0xff</span>) <span class="kw">as</span> <span class="ident">i16</span>;
<span class="kw">let</span> <span class="ident">mantissa</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">exponent</span> <span class="op">==</span> <span class="number">0</span> {
(<span class="ident">bits</span> <span class="op">&</span> <span class="number">0x7fffff</span>) <span class="op"><<</span> <span class="number">1</span>
} <span class="kw">else</span> {
(<span class="ident">bits</span> <span class="op">&</span> <span class="number">0x7fffff</span>) <span class="op">|</span> <span class="number">0x800000</span>
};
<span class="comment">// Exponent bias + mantissa shift</span>
<span class="ident">exponent</span> <span class="op">-=</span> <span class="number">127</span> <span class="op">+</span> <span class="number">23</span>;
(<span class="ident">mantissa</span> <span class="kw">as</span> <span class="ident">u64</span>, <span class="ident">exponent</span>, <span class="ident">sign</span>)
}
<span class="kw">fn</span> <span class="ident">integer_decode_f64</span>(<span class="ident">f</span>: <span class="ident">f64</span>) <span class="op">-></span> (<span class="ident">u64</span>, <span class="ident">i16</span>, <span class="ident">i8</span>) {
<span class="kw">let</span> <span class="ident">bits</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">mem</span>::<span class="ident">transmute</span>(<span class="ident">f</span>) };
<span class="kw">let</span> <span class="ident">sign</span>: <span class="ident">i8</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">bits</span> <span class="op">>></span> <span class="number">63</span> <span class="op">==</span> <span class="number">0</span> {
<span class="number">1</span>
} <span class="kw">else</span> {
<span class="op">-</span><span class="number">1</span>
};
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">exponent</span>: <span class="ident">i16</span> <span class="op">=</span> ((<span class="ident">bits</span> <span class="op">>></span> <span class="number">52</span>) <span class="op">&</span> <span class="number">0x7ff</span>) <span class="kw">as</span> <span class="ident">i16</span>;
<span class="kw">let</span> <span class="ident">mantissa</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">exponent</span> <span class="op">==</span> <span class="number">0</span> {
(<span class="ident">bits</span> <span class="op">&</span> <span class="number">0xfffffffffffff</span>) <span class="op"><<</span> <span class="number">1</span>
} <span class="kw">else</span> {
(<span class="ident">bits</span> <span class="op">&</span> <span class="number">0xfffffffffffff</span>) <span class="op">|</span> <span class="number">0x10000000000000</span>
};
<span class="comment">// Exponent bias + mantissa shift</span>
<span class="ident">exponent</span> <span class="op">-=</span> <span class="number">1023</span> <span class="op">+</span> <span class="number">52</span>;
(<span class="ident">mantissa</span>, <span class="ident">exponent</span>, <span class="ident">sign</span>)
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>)]</span>
<span class="macro">float_impl</span><span class="macro">!</span>(<span class="ident">f32</span> <span class="ident">integer_decode_f32</span>);
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>)]</span>
<span class="macro">float_impl</span><span class="macro">!</span>(<span class="ident">f64</span> <span class="ident">integer_decode_f64</span>);
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">float_const_impl</span> {
($(<span class="attribute">#[<span class="macro-nonterminal">$</span><span class="macro-nonterminal">doc</span>:<span class="ident">meta</span>]</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">constant</span>:<span class="ident">ident</span>,)<span class="op">+</span>) <span class="op">=></span> (
<span class="attribute">#[<span class="ident">allow</span>(<span class="ident">non_snake_case</span>)]</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">FloatConst</span> {
$(<span class="attribute">#[<span class="macro-nonterminal">$</span><span class="macro-nonterminal">doc</span>]</span> <span class="kw">fn</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">constant</span>() <span class="op">-></span> <span class="self">Self</span>;)<span class="op">+</span>
}
<span class="macro">float_const_impl</span><span class="macro">!</span> { @<span class="ident">float</span> <span class="ident">f32</span>, $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">constant</span>,)<span class="op">+</span> }
<span class="macro">float_const_impl</span><span class="macro">!</span> { @<span class="ident">float</span> <span class="ident">f64</span>, $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">constant</span>,)<span class="op">+</span> }
);
(@<span class="ident">float</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>:<span class="ident">ident</span>, $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">constant</span>:<span class="ident">ident</span>,)<span class="op">+</span>) <span class="op">=></span> (
<span class="kw">impl</span> <span class="ident">FloatConst</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span> {
<span class="macro">constant</span><span class="macro">!</span> {
$( <span class="macro-nonterminal">$</span><span class="macro-nonterminal">constant</span>() <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>::<span class="ident">consts</span>::<span class="macro-nonterminal">$</span><span class="macro-nonterminal">constant</span>; )<span class="op">+</span>
}
}
);
}
<span class="macro">float_const_impl</span><span class="macro">!</span> {
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return Euler’s number."</span>]</span>
<span class="ident">E</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `1.0 / π`."</span>]</span>
<span class="ident">FRAC_1_PI</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `1.0 / sqrt(2.0)`."</span>]</span>
<span class="ident">FRAC_1_SQRT_2</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `2.0 / π`."</span>]</span>
<span class="ident">FRAC_2_PI</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `2.0 / sqrt(π)`."</span>]</span>
<span class="ident">FRAC_2_SQRT_PI</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `π / 2.0`."</span>]</span>
<span class="ident">FRAC_PI_2</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `π / 3.0`."</span>]</span>
<span class="ident">FRAC_PI_3</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `π / 4.0`."</span>]</span>
<span class="ident">FRAC_PI_4</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `π / 6.0`."</span>]</span>
<span class="ident">FRAC_PI_6</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `π / 8.0`."</span>]</span>
<span class="ident">FRAC_PI_8</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `ln(10.0)`."</span>]</span>
<span class="ident">LN_10</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `ln(2.0)`."</span>]</span>
<span class="ident">LN_2</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `log10(e)`."</span>]</span>
<span class="ident">LOG10_E</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `log2(e)`."</span>]</span>
<span class="ident">LOG2_E</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return Archimedes’ constant."</span>]</span>
<span class="ident">PI</span>,
<span class="attribute">#[<span class="ident">doc</span> <span class="op">=</span> <span class="string">"Return `sqrt(2.0)`."</span>]</span>
<span class="ident">SQRT_2</span>,
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">mod</span> <span class="ident">tests</span> {
<span class="kw">use</span> <span class="ident">core</span>::<span class="ident">f64</span>::<span class="ident">consts</span>;
<span class="kw">const</span> <span class="ident">DEG_RAD_PAIRS</span>: [(<span class="ident">f64</span>, <span class="ident">f64</span>); <span class="number">7</span>] <span class="op">=</span> [
(<span class="number">0.0</span>, <span class="number">0.</span>),
(<span class="number">22.5</span>, <span class="ident">consts</span>::<span class="ident">FRAC_PI_8</span>),
(<span class="number">30.0</span>, <span class="ident">consts</span>::<span class="ident">FRAC_PI_6</span>),
(<span class="number">45.0</span>, <span class="ident">consts</span>::<span class="ident">FRAC_PI_4</span>),
(<span class="number">60.0</span>, <span class="ident">consts</span>::<span class="ident">FRAC_PI_3</span>),
(<span class="number">90.0</span>, <span class="ident">consts</span>::<span class="ident">FRAC_PI_2</span>),
(<span class="number">180.0</span>, <span class="ident">consts</span>::<span class="ident">PI</span>),
];
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">convert_deg_rad</span>() {
<span class="kw">use</span> <span class="ident">float</span>::<span class="ident">FloatCore</span>;
<span class="kw">for</span> <span class="kw-2">&</span>(<span class="ident">deg</span>, <span class="ident">rad</span>) <span class="kw">in</span> <span class="kw-2">&</span><span class="ident">DEG_RAD_PAIRS</span> {
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">FloatCore</span>::<span class="ident">to_degrees</span>(<span class="ident">rad</span>) <span class="op">-</span> <span class="ident">deg</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="number">1e-6</span>);
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">FloatCore</span>::<span class="ident">to_radians</span>(<span class="ident">deg</span>) <span class="op">-</span> <span class="ident">rad</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="number">1e-6</span>);
<span class="kw">let</span> (<span class="ident">deg</span>, <span class="ident">rad</span>) <span class="op">=</span> (<span class="ident">deg</span> <span class="kw">as</span> <span class="ident">f32</span>, <span class="ident">rad</span> <span class="kw">as</span> <span class="ident">f32</span>);
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">FloatCore</span>::<span class="ident">to_degrees</span>(<span class="ident">rad</span>) <span class="op">-</span> <span class="ident">deg</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="number">1e-5</span>);
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">FloatCore</span>::<span class="ident">to_radians</span>(<span class="ident">deg</span>) <span class="op">-</span> <span class="ident">rad</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="number">1e-5</span>);
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>)]</span>
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">convert_deg_rad_std</span>() {
<span class="kw">for</span> <span class="kw-2">&</span>(<span class="ident">deg</span>, <span class="ident">rad</span>) <span class="kw">in</span> <span class="kw-2">&</span><span class="ident">DEG_RAD_PAIRS</span> {
<span class="kw">use</span> <span class="ident">Float</span>;
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">Float</span>::<span class="ident">to_degrees</span>(<span class="ident">rad</span>) <span class="op">-</span> <span class="ident">deg</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="number">1e-6</span>);
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">Float</span>::<span class="ident">to_radians</span>(<span class="ident">deg</span>) <span class="op">-</span> <span class="ident">rad</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="number">1e-6</span>);
<span class="kw">let</span> (<span class="ident">deg</span>, <span class="ident">rad</span>) <span class="op">=</span> (<span class="ident">deg</span> <span class="kw">as</span> <span class="ident">f32</span>, <span class="ident">rad</span> <span class="kw">as</span> <span class="ident">f32</span>);
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">Float</span>::<span class="ident">to_degrees</span>(<span class="ident">rad</span>) <span class="op">-</span> <span class="ident">deg</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="number">1e-5</span>);
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">Float</span>::<span class="ident">to_radians</span>(<span class="ident">deg</span>) <span class="op">-</span> <span class="ident">rad</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="number">1e-5</span>);
}
}
}
</pre>
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