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</pre><pre class='rust '>
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>mem</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>ops</span>::<span class='ident'>Neg</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>num</span>::<span class='ident'>FpCategory</span>;
<span class='kw'>use</span> {<span class='ident'>Num</span>, <span class='ident'>NumCast</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 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` and</span>
<span class='doccomment'>/// `Float::infinity()`.</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_positive());</span>
<span class='doccomment'>/// assert!(!g.is_sign_positive());</span>
<span class='doccomment'>/// // Requires both tests to determine if is `NaN`</span>
<span class='doccomment'>/// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());</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` and</span>
<span class='doccomment'>/// `Float::neg_infinity()`.</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'>///</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'>/// // Requires both tests to determine if is `NaN`.</span>
<span class='doccomment'>/// assert!(!nan.is_sign_positive() && !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'>/// 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'>/// The floating point encoding is documented in the [Reference][floating-point].</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='doccomment'>/// [floating-point]: ../../../../../reference.html#machine-types</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'>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'>$</span><span class='macro-nonterminal'>T</span> {
<span class='kw'>fn</span> <span class='ident'>nan</span>() <span class='op'>-></span> <span class='self'>Self</span> {
::<span class='ident'>std</span>::<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span>::<span class='ident'>NAN</span>
}
<span class='kw'>fn</span> <span class='ident'>infinity</span>() <span class='op'>-></span> <span class='self'>Self</span> {
::<span class='ident'>std</span>::<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span>::<span class='ident'>INFINITY</span>
}
<span class='kw'>fn</span> <span class='ident'>neg_infinity</span>() <span class='op'>-></span> <span class='self'>Self</span> {
::<span class='ident'>std</span>::<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span>::<span class='ident'>NEG_INFINITY</span>
}
<span class='kw'>fn</span> <span class='ident'>neg_zero</span>() <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'>-</span><span class='number'>0.0</span>
}
<span class='kw'>fn</span> <span class='ident'>min_value</span>() <span class='op'>-></span> <span class='self'>Self</span> {
::<span class='ident'>std</span>::<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span>::<span class='ident'>MIN</span>
}
<span class='kw'>fn</span> <span class='ident'>min_positive_value</span>() <span class='op'>-></span> <span class='self'>Self</span> {
::<span class='ident'>std</span>::<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span>::<span class='ident'>MIN_POSITIVE</span>
}
<span class='kw'>fn</span> <span class='ident'>max_value</span>() <span class='op'>-></span> <span class='self'>Self</span> {
::<span class='ident'>std</span>::<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span>::<span class='ident'>MAX</span>
}
<span class='kw'>fn</span> <span class='ident'>is_nan</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>is_nan</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>is_infinite</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>is_finite</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>is_finite</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>is_normal</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>classify</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>FpCategory</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>classify</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>floor</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>ceil</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>ceil</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>round</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>trunc</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>trunc</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>fract</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>abs</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>abs</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>signum</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>is_sign_positive</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>is_sign_positive</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>is_sign_negative</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>mul_add</span>(<span class='self'>self</span>, <span class='ident'>a</span>: <span class='self'>Self</span>, <span class='ident'>b</span>: <span class='self'>Self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>mul_add</span>(<span class='self'>self</span>, <span class='ident'>a</span>, <span class='ident'>b</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>recip</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>powi</span>(<span class='self'>self</span>, <span class='ident'>n</span>: <span class='ident'>i32</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>powi</span>(<span class='self'>self</span>, <span class='ident'>n</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>powf</span>(<span class='self'>self</span>, <span class='ident'>n</span>)
}
<span class='kw'>fn</span> <span class='ident'>sqrt</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>sqrt</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>exp</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>exp2</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>exp2</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>ln</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>log</span>(<span class='self'>self</span>, <span class='ident'>base</span>: <span class='self'>Self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>log</span>(<span class='self'>self</span>, <span class='ident'>base</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>log2</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>log10</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>log10</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>max</span>(<span class='self'>self</span>, <span class='ident'>other</span>)
}
<span class='kw'>fn</span> <span class='ident'>min</span>(<span class='self'>self</span>, <span class='ident'>other</span>: <span class='self'>Self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>min</span>(<span class='self'>self</span>, <span class='ident'>other</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'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>abs_sub</span>(<span class='self'>self</span>, <span class='ident'>other</span>)
}
<span class='kw'>fn</span> <span class='ident'>cbrt</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>cbrt</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>hypot</span>(<span class='self'>self</span>, <span class='ident'>other</span>)
}
<span class='kw'>fn</span> <span class='ident'>sin</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>sin</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>cos</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>tan</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>tan</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>asin</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>acos</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>acos</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>atan</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>atan2</span>(<span class='self'>self</span>, <span class='ident'>other</span>: <span class='self'>Self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>atan2</span>(<span class='self'>self</span>, <span class='ident'>other</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>sin_cos</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>exp_m1</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>exp_m1</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>ln_1p</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>sinh</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>sinh</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>cosh</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>tanh</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>tanh</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>asinh</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>acosh</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>acosh</span>(<span class='self'>self</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='op'><</span><span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>T</span><span class='op'>></span>::<span class='ident'>atanh</span>(<span class='self'>self</span>)
}
<span class='kw'>fn</span> <span class='ident'>integer_decode</span>(<span class='self'>self</span>) <span class='op'>-></span> (<span class='ident'>u64</span>, <span class='ident'>i16</span>, <span class='ident'>i8</span>) {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>decode</span>(<span class='self'>self</span>)
}
}
)
}
<span class='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='kw-2'>&</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='kw-2'>&</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='kw-2'>&</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='kw-2'>&</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='kw-2'>&</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='kw-2'>&</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='macro'>float_impl</span><span class='macro'>!</span>(<span class='ident'>f32</span> <span class='ident'>integer_decode_f32</span>);
<span class='macro'>float_impl</span><span class='macro'>!</span>(<span class='ident'>f64</span> <span class='ident'>integer_decode_f64</span>);
</pre>
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