vendor/num-traits-0.2.19/src/real.rs - toolchain/rustc - Git at Google

 #![cfg(any(feature = "std", feature = "libm"))]

 use core::ops::Neg;

 use crate::{Float, Num, NumCast};

 // NOTE: These doctests have the same issue as those in src/float.rs.
 // They're testing the inherent methods directly, and not those of `Real`.

 /// A trait for real number types that do not necessarily have
 /// floating-point-specific characteristics such as NaN and infinity.
 ///
 /// See [this Wikipedia article](https://en.wikipedia.org/wiki/Real_data_type)
 /// for a list of data types that could meaningfully implement this trait.
 ///
 /// This trait is only available with the `std` feature, or with the `libm` feature otherwise.
 pub trait Real: Num + Copy + NumCast + PartialOrd + Neg<Output = Self> {
     /// Returns the smallest finite value that this type can represent.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let x: f64 = Real::min_value();
     ///
     /// assert_eq!(x, f64::MIN);
     /// ```
     fn min_value() -> Self;

     /// Returns the smallest positive, normalized value that this type can represent.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let x: f64 = Real::min_positive_value();
     ///
     /// assert_eq!(x, f64::MIN_POSITIVE);
     /// ```
     fn min_positive_value() -> Self;

     /// Returns epsilon, a small positive value.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let x: f64 = Real::epsilon();
     ///
     /// assert_eq!(x, f64::EPSILON);
     /// ```
     ///
     /// # Panics
     ///
     /// The default implementation will panic if `f32::EPSILON` cannot
     /// be cast to `Self`.
     fn epsilon() -> Self;

     /// Returns the largest finite value that this type can represent.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let x: f64 = Real::max_value();
     /// assert_eq!(x, f64::MAX);
     /// ```
     fn max_value() -> Self;

     /// Returns the largest integer less than or equal to a number.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let f = 3.99;
     /// let g = 3.0;
     ///
     /// assert_eq!(f.floor(), 3.0);
     /// assert_eq!(g.floor(), 3.0);
     /// ```
     fn floor(self) -> Self;

     /// Returns the smallest integer greater than or equal to a number.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let f = 3.01;
     /// let g = 4.0;
     ///
     /// assert_eq!(f.ceil(), 4.0);
     /// assert_eq!(g.ceil(), 4.0);
     /// ```
     fn ceil(self) -> Self;

     /// Returns the nearest integer to a number. Round half-way cases away from
     /// `0.0`.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let f = 3.3;
     /// let g = -3.3;
     ///
     /// assert_eq!(f.round(), 3.0);
     /// assert_eq!(g.round(), -3.0);
     /// ```
     fn round(self) -> Self;

     /// Return the integer part of a number.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let f = 3.3;
     /// let g = -3.7;
     ///
     /// assert_eq!(f.trunc(), 3.0);
     /// assert_eq!(g.trunc(), -3.0);
     /// ```
     fn trunc(self) -> Self;

     /// Returns the fractional part of a number.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 3.5;
     /// let y = -3.5;
     /// let abs_difference_x = (x.fract() - 0.5).abs();
     /// let abs_difference_y = (y.fract() - (-0.5)).abs();
     ///
     /// assert!(abs_difference_x < 1e-10);
     /// assert!(abs_difference_y < 1e-10);
     /// ```
     fn fract(self) -> Self;

     /// Computes the absolute value of `self`. Returns `Float::nan()` if the
     /// number is `Float::nan()`.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let x = 3.5;
     /// let y = -3.5;
     ///
     /// let abs_difference_x = (x.abs() - x).abs();
     /// let abs_difference_y = (y.abs() - (-y)).abs();
     ///
     /// assert!(abs_difference_x < 1e-10);
     /// assert!(abs_difference_y < 1e-10);
     ///
     /// assert!(::num_traits::Float::is_nan(f64::NAN.abs()));
     /// ```
     fn abs(self) -> Self;

     /// Returns a number that represents the sign of `self`.
     ///
     /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
     /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
     /// - `Float::nan()` if the number is `Float::nan()`
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let f = 3.5;
     ///
     /// assert_eq!(f.signum(), 1.0);
     /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
     ///
     /// assert!(f64::NAN.signum().is_nan());
     /// ```
     fn signum(self) -> Self;

     /// Returns `true` if `self` is positive, including `+0.0`,
     /// `Float::infinity()`, and with newer versions of Rust `f64::NAN`.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let neg_nan: f64 = -f64::NAN;
     ///
     /// let f = 7.0;
     /// let g = -7.0;
     ///
     /// assert!(f.is_sign_positive());
     /// assert!(!g.is_sign_positive());
     /// assert!(!neg_nan.is_sign_positive());
     /// ```
     fn is_sign_positive(self) -> bool;

     /// Returns `true` if `self` is negative, including `-0.0`,
     /// `Float::neg_infinity()`, and with newer versions of Rust `-f64::NAN`.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let nan: f64 = f64::NAN;
     ///
     /// let f = 7.0;
     /// let g = -7.0;
     ///
     /// assert!(!f.is_sign_negative());
     /// assert!(g.is_sign_negative());
     /// assert!(!nan.is_sign_negative());
     /// ```
     fn is_sign_negative(self) -> bool;

     /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
     /// error, yielding a more accurate result than an unfused multiply-add.
     ///
     /// Using `mul_add` can be more performant than an unfused multiply-add if
     /// the target architecture has a dedicated `fma` CPU instruction.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let m = 10.0;
     /// let x = 4.0;
     /// let b = 60.0;
     ///
     /// // 100.0
     /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn mul_add(self, a: Self, b: Self) -> Self;

     /// Take the reciprocal (inverse) of a number, `1/x`.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 2.0;
     /// let abs_difference = (x.recip() - (1.0/x)).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn recip(self) -> Self;

     /// Raise a number to an integer power.
     ///
     /// Using this function is generally faster than using `powf`
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 2.0;
     /// let abs_difference = (x.powi(2) - x*x).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn powi(self, n: i32) -> Self;

     /// Raise a number to a real number power.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 2.0;
     /// let abs_difference = (x.powf(2.0) - x*x).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn powf(self, n: Self) -> Self;

     /// Take the square root of a number.
     ///
     /// Returns NaN if `self` is a negative floating-point number.
     ///
     /// # Panics
     ///
     /// If the implementing type doesn't support NaN, this method should panic if `self < 0`.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let positive = 4.0;
     /// let negative = -4.0;
     ///
     /// let abs_difference = (positive.sqrt() - 2.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// assert!(::num_traits::Float::is_nan(negative.sqrt()));
     /// ```
     fn sqrt(self) -> Self;

     /// Returns `e^(self)`, (the exponential function).
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let one = 1.0;
     /// // e^1
     /// let e = one.exp();
     ///
     /// // ln(e) - 1 == 0
     /// let abs_difference = (e.ln() - 1.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn exp(self) -> Self;

     /// Returns `2^(self)`.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let f = 2.0;
     ///
     /// // 2^2 - 4 == 0
     /// let abs_difference = (f.exp2() - 4.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn exp2(self) -> Self;

     /// Returns the natural logarithm of the number.
     ///
     /// # Panics
     ///
     /// If `self <= 0` and this type does not support a NaN representation, this function should panic.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let one = 1.0;
     /// // e^1
     /// let e = one.exp();
     ///
     /// // ln(e) - 1 == 0
     /// let abs_difference = (e.ln() - 1.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn ln(self) -> Self;

     /// Returns the logarithm of the number with respect to an arbitrary base.
     ///
     /// # Panics
     ///
     /// If `self <= 0` and this type does not support a NaN representation, this function should panic.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let ten = 10.0;
     /// let two = 2.0;
     ///
     /// // log10(10) - 1 == 0
     /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
     ///
     /// // log2(2) - 1 == 0
     /// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
     ///
     /// assert!(abs_difference_10 < 1e-10);
     /// assert!(abs_difference_2 < 1e-10);
     /// ```
     fn log(self, base: Self) -> Self;

     /// Returns the base 2 logarithm of the number.
     ///
     /// # Panics
     ///
     /// If `self <= 0` and this type does not support a NaN representation, this function should panic.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let two = 2.0;
     ///
     /// // log2(2) - 1 == 0
     /// let abs_difference = (two.log2() - 1.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn log2(self) -> Self;

     /// Returns the base 10 logarithm of the number.
     ///
     /// # Panics
     ///
     /// If `self <= 0` and this type does not support a NaN representation, this function should panic.
     ///
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let ten = 10.0;
     ///
     /// // log10(10) - 1 == 0
     /// let abs_difference = (ten.log10() - 1.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn log10(self) -> Self;

     /// Converts radians to degrees.
     ///
     /// ```
     /// use std::f64::consts;
     ///
     /// let angle = consts::PI;
     ///
     /// let abs_difference = (angle.to_degrees() - 180.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn to_degrees(self) -> Self;

     /// Converts degrees to radians.
     ///
     /// ```
     /// use std::f64::consts;
     ///
     /// let angle = 180.0_f64;
     ///
     /// let abs_difference = (angle.to_radians() - consts::PI).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn to_radians(self) -> Self;

     /// Returns the maximum of the two numbers.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 1.0;
     /// let y = 2.0;
     ///
     /// assert_eq!(x.max(y), y);
     /// ```
     fn max(self, other: Self) -> Self;

     /// Returns the minimum of the two numbers.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 1.0;
     /// let y = 2.0;
     ///
     /// assert_eq!(x.min(y), x);
     /// ```
     fn min(self, other: Self) -> Self;

     /// The positive difference of two numbers.
     ///
     /// * If `self <= other`: `0:0`
     /// * Else: `self - other`
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 3.0;
     /// let y = -3.0;
     ///
     /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
     /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
     ///
     /// assert!(abs_difference_x < 1e-10);
     /// assert!(abs_difference_y < 1e-10);
     /// ```
     fn abs_sub(self, other: Self) -> Self;

     /// Take the cubic root of a number.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 8.0;
     ///
     /// // x^(1/3) - 2 == 0
     /// let abs_difference = (x.cbrt() - 2.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn cbrt(self) -> Self;

     /// Calculate the length of the hypotenuse of a right-angle triangle given
     /// legs of length `x` and `y`.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 2.0;
     /// let y = 3.0;
     ///
     /// // sqrt(x^2 + y^2)
     /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn hypot(self, other: Self) -> Self;

     /// Computes the sine of a number (in radians).
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let x = f64::consts::PI/2.0;
     ///
     /// let abs_difference = (x.sin() - 1.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn sin(self) -> Self;

     /// Computes the cosine of a number (in radians).
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let x = 2.0*f64::consts::PI;
     ///
     /// let abs_difference = (x.cos() - 1.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn cos(self) -> Self;

     /// Computes the tangent of a number (in radians).
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let x = f64::consts::PI/4.0;
     /// let abs_difference = (x.tan() - 1.0).abs();
     ///
     /// assert!(abs_difference < 1e-14);
     /// ```
     fn tan(self) -> Self;

     /// Computes the arcsine of a number. Return value is in radians in
     /// the range [-pi/2, pi/2] or NaN if the number is outside the range
     /// [-1, 1].
     ///
     /// # Panics
     ///
     /// If this type does not support a NaN representation, this function should panic
     /// if the number is outside the range [-1, 1].
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let f = f64::consts::PI / 2.0;
     ///
     /// // asin(sin(pi/2))
     /// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn asin(self) -> Self;

     /// Computes the arccosine of a number. Return value is in radians in
     /// the range [0, pi] or NaN if the number is outside the range
     /// [-1, 1].
     ///
     /// # Panics
     ///
     /// If this type does not support a NaN representation, this function should panic
     /// if the number is outside the range [-1, 1].
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let f = f64::consts::PI / 4.0;
     ///
     /// // acos(cos(pi/4))
     /// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn acos(self) -> Self;

     /// Computes the arctangent of a number. Return value is in radians in the
     /// range [-pi/2, pi/2];
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let f = 1.0;
     ///
     /// // atan(tan(1))
     /// let abs_difference = (f.tan().atan() - 1.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn atan(self) -> Self;

     /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
     ///
     /// * `x = 0`, `y = 0`: `0`
     /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
     /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
     /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let pi = f64::consts::PI;
     /// // All angles from horizontal right (+x)
     /// // 45 deg counter-clockwise
     /// let x1 = 3.0;
     /// let y1 = -3.0;
     ///
     /// // 135 deg clockwise
     /// let x2 = -3.0;
     /// let y2 = 3.0;
     ///
     /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
     /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
     ///
     /// assert!(abs_difference_1 < 1e-10);
     /// assert!(abs_difference_2 < 1e-10);
     /// ```
     fn atan2(self, other: Self) -> Self;

     /// Simultaneously computes the sine and cosine of the number, `x`. Returns
     /// `(sin(x), cos(x))`.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let x = f64::consts::PI/4.0;
     /// let f = x.sin_cos();
     ///
     /// let abs_difference_0 = (f.0 - x.sin()).abs();
     /// let abs_difference_1 = (f.1 - x.cos()).abs();
     ///
     /// assert!(abs_difference_0 < 1e-10);
     /// assert!(abs_difference_0 < 1e-10);
     /// ```
     fn sin_cos(self) -> (Self, Self);

     /// Returns `e^(self) - 1` in a way that is accurate even if the
     /// number is close to zero.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 7.0;
     ///
     /// // e^(ln(7)) - 1
     /// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn exp_m1(self) -> Self;

     /// Returns `ln(1+n)` (natural logarithm) more accurately than if
     /// the operations were performed separately.
     ///
     /// # Panics
     ///
     /// If this type does not support a NaN representation, this function should panic
     /// if `self-1 <= 0`.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let x = f64::consts::E - 1.0;
     ///
     /// // ln(1 + (e - 1)) == ln(e) == 1
     /// let abs_difference = (x.ln_1p() - 1.0).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn ln_1p(self) -> Self;

     /// Hyperbolic sine function.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let e = f64::consts::E;
     /// let x = 1.0;
     ///
     /// let f = x.sinh();
     /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
     /// let g = (e*e - 1.0)/(2.0*e);
     /// let abs_difference = (f - g).abs();
     ///
     /// assert!(abs_difference < 1e-10);
     /// ```
     fn sinh(self) -> Self;

     /// Hyperbolic cosine function.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let e = f64::consts::E;
     /// let x = 1.0;
     /// let f = x.cosh();
     /// // Solving cosh() at 1 gives this result
     /// let g = (e*e + 1.0)/(2.0*e);
     /// let abs_difference = (f - g).abs();
     ///
     /// // Same result
     /// assert!(abs_difference < 1.0e-10);
     /// ```
     fn cosh(self) -> Self;

     /// Hyperbolic tangent function.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let e = f64::consts::E;
     /// let x = 1.0;
     ///
     /// let f = x.tanh();
     /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
     /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
     /// let abs_difference = (f - g).abs();
     ///
     /// assert!(abs_difference < 1.0e-10);
     /// ```
     fn tanh(self) -> Self;

     /// Inverse hyperbolic sine function.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 1.0;
     /// let f = x.sinh().asinh();
     ///
     /// let abs_difference = (f - x).abs();
     ///
     /// assert!(abs_difference < 1.0e-10);
     /// ```
     fn asinh(self) -> Self;

     /// Inverse hyperbolic cosine function.
     ///
     /// ```
     /// use num_traits::real::Real;
     ///
     /// let x = 1.0;
     /// let f = x.cosh().acosh();
     ///
     /// let abs_difference = (f - x).abs();
     ///
     /// assert!(abs_difference < 1.0e-10);
     /// ```
     fn acosh(self) -> Self;

     /// Inverse hyperbolic tangent function.
     ///
     /// ```
     /// use num_traits::real::Real;
     /// use std::f64;
     ///
     /// let e = f64::consts::E;
     /// let f = e.tanh().atanh();
     ///
     /// let abs_difference = (f - e).abs();
     ///
     /// assert!(abs_difference < 1.0e-10);
     /// ```
     fn atanh(self) -> Self;
 }

 impl<T: Float> Real for T {
     forward! {
         Float::min_value() -> Self;
         Float::min_positive_value() -> Self;
         Float::epsilon() -> Self;
         Float::max_value() -> Self;
     }
     forward! {
         Float::floor(self) -> Self;
         Float::ceil(self) -> Self;
         Float::round(self) -> Self;
         Float::trunc(self) -> Self;
         Float::fract(self) -> Self;
         Float::abs(self) -> Self;
         Float::signum(self) -> Self;
         Float::is_sign_positive(self) -> bool;
         Float::is_sign_negative(self) -> bool;
         Float::mul_add(self, a: Self, b: Self) -> Self;
         Float::recip(self) -> Self;
         Float::powi(self, n: i32) -> Self;
         Float::powf(self, n: Self) -> Self;
         Float::sqrt(self) -> Self;
         Float::exp(self) -> Self;
         Float::exp2(self) -> Self;
         Float::ln(self) -> Self;
         Float::log(self, base: Self) -> Self;
         Float::log2(self) -> Self;
         Float::log10(self) -> Self;
         Float::to_degrees(self) -> Self;
         Float::to_radians(self) -> Self;
         Float::max(self, other: Self) -> Self;
         Float::min(self, other: Self) -> Self;
         Float::abs_sub(self, other: Self) -> Self;
         Float::cbrt(self) -> Self;
         Float::hypot(self, other: Self) -> Self;
         Float::sin(self) -> Self;
         Float::cos(self) -> Self;
         Float::tan(self) -> Self;
         Float::asin(self) -> Self;
         Float::acos(self) -> Self;
         Float::atan(self) -> Self;
         Float::atan2(self, other: Self) -> Self;
         Float::sin_cos(self) -> (Self, Self);
         Float::exp_m1(self) -> Self;
         Float::ln_1p(self) -> Self;
         Float::sinh(self) -> Self;
         Float::cosh(self) -> Self;
         Float::tanh(self) -> Self;
         Float::asinh(self) -> Self;
         Float::acosh(self) -> Self;
         Float::atanh(self) -> Self;
     }
 }
	#![cfg(any(feature = "std", feature = "libm"))]

	use core::ops::Neg;

	use crate::{Float, Num, NumCast};

	// NOTE: These doctests have the same issue as those in src/float.rs.
	// They're testing the inherent methods directly, and not those of `Real`.

	/// A trait for real number types that do not necessarily have
	/// floating-point-specific characteristics such as NaN and infinity.
	///
	/// See [this Wikipedia article](https://en.wikipedia.org/wiki/Real_data_type)
	/// for a list of data types that could meaningfully implement this trait.
	///
	/// This trait is only available with the `std` feature, or with the `libm` feature otherwise.
	pub trait Real: Num + Copy + NumCast + PartialOrd + Neg<Output = Self> {
	/// Returns the smallest finite value that this type can represent.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let x: f64 = Real::min_value();
	///
	/// assert_eq!(x, f64::MIN);
	/// ```
	fn min_value() -> Self;

	/// Returns the smallest positive, normalized value that this type can represent.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let x: f64 = Real::min_positive_value();
	///
	/// assert_eq!(x, f64::MIN_POSITIVE);
	/// ```
	fn min_positive_value() -> Self;

	/// Returns epsilon, a small positive value.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let x: f64 = Real::epsilon();
	///
	/// assert_eq!(x, f64::EPSILON);
	/// ```
	///
	/// # Panics
	///
	/// The default implementation will panic if `f32::EPSILON` cannot
	/// be cast to `Self`.
	fn epsilon() -> Self;

	/// Returns the largest finite value that this type can represent.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let x: f64 = Real::max_value();
	/// assert_eq!(x, f64::MAX);
	/// ```
	fn max_value() -> Self;

	/// Returns the largest integer less than or equal to a number.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let f = 3.99;
	/// let g = 3.0;
	///
	/// assert_eq!(f.floor(), 3.0);
	/// assert_eq!(g.floor(), 3.0);
	/// ```
	fn floor(self) -> Self;

	/// Returns the smallest integer greater than or equal to a number.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let f = 3.01;
	/// let g = 4.0;
	///
	/// assert_eq!(f.ceil(), 4.0);
	/// assert_eq!(g.ceil(), 4.0);
	/// ```
	fn ceil(self) -> Self;

	/// Returns the nearest integer to a number. Round half-way cases away from
	/// `0.0`.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let f = 3.3;
	/// let g = -3.3;
	///
	/// assert_eq!(f.round(), 3.0);
	/// assert_eq!(g.round(), -3.0);
	/// ```
	fn round(self) -> Self;

	/// Return the integer part of a number.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let f = 3.3;
	/// let g = -3.7;
	///
	/// assert_eq!(f.trunc(), 3.0);
	/// assert_eq!(g.trunc(), -3.0);
	/// ```
	fn trunc(self) -> Self;

	/// Returns the fractional part of a number.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 3.5;
	/// let y = -3.5;
	/// let abs_difference_x = (x.fract() - 0.5).abs();
	/// let abs_difference_y = (y.fract() - (-0.5)).abs();
	///
	/// assert!(abs_difference_x < 1e-10);
	/// assert!(abs_difference_y < 1e-10);
	/// ```
	fn fract(self) -> Self;

	/// Computes the absolute value of `self`. Returns `Float::nan()` if the
	/// number is `Float::nan()`.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let x = 3.5;
	/// let y = -3.5;
	///
	/// let abs_difference_x = (x.abs() - x).abs();
	/// let abs_difference_y = (y.abs() - (-y)).abs();
	///
	/// assert!(abs_difference_x < 1e-10);
	/// assert!(abs_difference_y < 1e-10);
	///
	/// assert!(::num_traits::Float::is_nan(f64::NAN.abs()));
	/// ```
	fn abs(self) -> Self;

	/// Returns a number that represents the sign of `self`.
	///
	/// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
	/// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
	/// - `Float::nan()` if the number is `Float::nan()`
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let f = 3.5;
	///
	/// assert_eq!(f.signum(), 1.0);
	/// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
	///
	/// assert!(f64::NAN.signum().is_nan());
	/// ```
	fn signum(self) -> Self;

	/// Returns `true` if `self` is positive, including `+0.0`,
	/// `Float::infinity()`, and with newer versions of Rust `f64::NAN`.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let neg_nan: f64 = -f64::NAN;
	///
	/// let f = 7.0;
	/// let g = -7.0;
	///
	/// assert!(f.is_sign_positive());
	/// assert!(!g.is_sign_positive());
	/// assert!(!neg_nan.is_sign_positive());
	/// ```
	fn is_sign_positive(self) -> bool;

	/// Returns `true` if `self` is negative, including `-0.0`,
	/// `Float::neg_infinity()`, and with newer versions of Rust `-f64::NAN`.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let nan: f64 = f64::NAN;
	///
	/// let f = 7.0;
	/// let g = -7.0;
	///
	/// assert!(!f.is_sign_negative());
	/// assert!(g.is_sign_negative());
	/// assert!(!nan.is_sign_negative());
	/// ```
	fn is_sign_negative(self) -> bool;

	/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
	/// error, yielding a more accurate result than an unfused multiply-add.
	///
	/// Using `mul_add` can be more performant than an unfused multiply-add if
	/// the target architecture has a dedicated `fma` CPU instruction.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let m = 10.0;
	/// let x = 4.0;
	/// let b = 60.0;
	///
	/// // 100.0
	/// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn mul_add(self, a: Self, b: Self) -> Self;

	/// Take the reciprocal (inverse) of a number, `1/x`.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 2.0;
	/// let abs_difference = (x.recip() - (1.0/x)).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn recip(self) -> Self;

	/// Raise a number to an integer power.
	///
	/// Using this function is generally faster than using `powf`
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 2.0;
	/// let abs_difference = (x.powi(2) - x*x).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn powi(self, n: i32) -> Self;

	/// Raise a number to a real number power.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 2.0;
	/// let abs_difference = (x.powf(2.0) - x*x).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn powf(self, n: Self) -> Self;

	/// Take the square root of a number.
	///
	/// Returns NaN if `self` is a negative floating-point number.
	///
	/// # Panics
	///
	/// If the implementing type doesn't support NaN, this method should panic if `self < 0`.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let positive = 4.0;
	/// let negative = -4.0;
	///
	/// let abs_difference = (positive.sqrt() - 2.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// assert!(::num_traits::Float::is_nan(negative.sqrt()));
	/// ```
	fn sqrt(self) -> Self;

	/// Returns `e^(self)`, (the exponential function).
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let one = 1.0;
	/// // e^1
	/// let e = one.exp();
	///
	/// // ln(e) - 1 == 0
	/// let abs_difference = (e.ln() - 1.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn exp(self) -> Self;

	/// Returns `2^(self)`.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let f = 2.0;
	///
	/// // 2^2 - 4 == 0
	/// let abs_difference = (f.exp2() - 4.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn exp2(self) -> Self;

	/// Returns the natural logarithm of the number.
	///
	/// # Panics
	///
	/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let one = 1.0;
	/// // e^1
	/// let e = one.exp();
	///
	/// // ln(e) - 1 == 0
	/// let abs_difference = (e.ln() - 1.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn ln(self) -> Self;

	/// Returns the logarithm of the number with respect to an arbitrary base.
	///
	/// # Panics
	///
	/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let ten = 10.0;
	/// let two = 2.0;
	///
	/// // log10(10) - 1 == 0
	/// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
	///
	/// // log2(2) - 1 == 0
	/// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
	///
	/// assert!(abs_difference_10 < 1e-10);
	/// assert!(abs_difference_2 < 1e-10);
	/// ```
	fn log(self, base: Self) -> Self;

	/// Returns the base 2 logarithm of the number.
	///
	/// # Panics
	///
	/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let two = 2.0;
	///
	/// // log2(2) - 1 == 0
	/// let abs_difference = (two.log2() - 1.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn log2(self) -> Self;

	/// Returns the base 10 logarithm of the number.
	///
	/// # Panics
	///
	/// If `self <= 0` and this type does not support a NaN representation, this function should panic.
	///
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let ten = 10.0;
	///
	/// // log10(10) - 1 == 0
	/// let abs_difference = (ten.log10() - 1.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn log10(self) -> Self;

	/// Converts radians to degrees.
	///
	/// ```
	/// use std::f64::consts;
	///
	/// let angle = consts::PI;
	///
	/// let abs_difference = (angle.to_degrees() - 180.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn to_degrees(self) -> Self;

	/// Converts degrees to radians.
	///
	/// ```
	/// use std::f64::consts;
	///
	/// let angle = 180.0_f64;
	///
	/// let abs_difference = (angle.to_radians() - consts::PI).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn to_radians(self) -> Self;

	/// Returns the maximum of the two numbers.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 1.0;
	/// let y = 2.0;
	///
	/// assert_eq!(x.max(y), y);
	/// ```
	fn max(self, other: Self) -> Self;

	/// Returns the minimum of the two numbers.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 1.0;
	/// let y = 2.0;
	///
	/// assert_eq!(x.min(y), x);
	/// ```
	fn min(self, other: Self) -> Self;

	/// The positive difference of two numbers.
	///
	/// * If `self <= other`: `0:0`
	/// * Else: `self - other`
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 3.0;
	/// let y = -3.0;
	///
	/// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
	/// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
	///
	/// assert!(abs_difference_x < 1e-10);
	/// assert!(abs_difference_y < 1e-10);
	/// ```
	fn abs_sub(self, other: Self) -> Self;

	/// Take the cubic root of a number.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 8.0;
	///
	/// // x^(1/3) - 2 == 0
	/// let abs_difference = (x.cbrt() - 2.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn cbrt(self) -> Self;

	/// Calculate the length of the hypotenuse of a right-angle triangle given
	/// legs of length `x` and `y`.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 2.0;
	/// let y = 3.0;
	///
	/// // sqrt(x^2 + y^2)
	/// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn hypot(self, other: Self) -> Self;

	/// Computes the sine of a number (in radians).
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let x = f64::consts::PI/2.0;
	///
	/// let abs_difference = (x.sin() - 1.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn sin(self) -> Self;

	/// Computes the cosine of a number (in radians).
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let x = 2.0*f64::consts::PI;
	///
	/// let abs_difference = (x.cos() - 1.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn cos(self) -> Self;

	/// Computes the tangent of a number (in radians).
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let x = f64::consts::PI/4.0;
	/// let abs_difference = (x.tan() - 1.0).abs();
	///
	/// assert!(abs_difference < 1e-14);
	/// ```
	fn tan(self) -> Self;

	/// Computes the arcsine of a number. Return value is in radians in
	/// the range [-pi/2, pi/2] or NaN if the number is outside the range
	/// [-1, 1].
	///
	/// # Panics
	///
	/// If this type does not support a NaN representation, this function should panic
	/// if the number is outside the range [-1, 1].
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let f = f64::consts::PI / 2.0;
	///
	/// // asin(sin(pi/2))
	/// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn asin(self) -> Self;

	/// Computes the arccosine of a number. Return value is in radians in
	/// the range [0, pi] or NaN if the number is outside the range
	/// [-1, 1].
	///
	/// # Panics
	///
	/// If this type does not support a NaN representation, this function should panic
	/// if the number is outside the range [-1, 1].
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let f = f64::consts::PI / 4.0;
	///
	/// // acos(cos(pi/4))
	/// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn acos(self) -> Self;

	/// Computes the arctangent of a number. Return value is in radians in the
	/// range [-pi/2, pi/2];
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let f = 1.0;
	///
	/// // atan(tan(1))
	/// let abs_difference = (f.tan().atan() - 1.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn atan(self) -> Self;

	/// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
	///
	/// * `x = 0`, `y = 0`: `0`
	/// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
	/// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
	/// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let pi = f64::consts::PI;
	/// // All angles from horizontal right (+x)
	/// // 45 deg counter-clockwise
	/// let x1 = 3.0;
	/// let y1 = -3.0;
	///
	/// // 135 deg clockwise
	/// let x2 = -3.0;
	/// let y2 = 3.0;
	///
	/// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
	/// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
	///
	/// assert!(abs_difference_1 < 1e-10);
	/// assert!(abs_difference_2 < 1e-10);
	/// ```
	fn atan2(self, other: Self) -> Self;

	/// Simultaneously computes the sine and cosine of the number, `x`. Returns
	/// `(sin(x), cos(x))`.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let x = f64::consts::PI/4.0;
	/// let f = x.sin_cos();
	///
	/// let abs_difference_0 = (f.0 - x.sin()).abs();
	/// let abs_difference_1 = (f.1 - x.cos()).abs();
	///
	/// assert!(abs_difference_0 < 1e-10);
	/// assert!(abs_difference_0 < 1e-10);
	/// ```
	fn sin_cos(self) -> (Self, Self);

	/// Returns `e^(self) - 1` in a way that is accurate even if the
	/// number is close to zero.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 7.0;
	///
	/// // e^(ln(7)) - 1
	/// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn exp_m1(self) -> Self;

	/// Returns `ln(1+n)` (natural logarithm) more accurately than if
	/// the operations were performed separately.
	///
	/// # Panics
	///
	/// If this type does not support a NaN representation, this function should panic
	/// if `self-1 <= 0`.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let x = f64::consts::E - 1.0;
	///
	/// // ln(1 + (e - 1)) == ln(e) == 1
	/// let abs_difference = (x.ln_1p() - 1.0).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn ln_1p(self) -> Self;

	/// Hyperbolic sine function.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let e = f64::consts::E;
	/// let x = 1.0;
	///
	/// let f = x.sinh();
	/// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
	/// let g = (ee - 1.0)/(2.0e);
	/// let abs_difference = (f - g).abs();
	///
	/// assert!(abs_difference < 1e-10);
	/// ```
	fn sinh(self) -> Self;

	/// Hyperbolic cosine function.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let e = f64::consts::E;
	/// let x = 1.0;
	/// let f = x.cosh();
	/// // Solving cosh() at 1 gives this result
	/// let g = (ee + 1.0)/(2.0e);
	/// let abs_difference = (f - g).abs();
	///
	/// // Same result
	/// assert!(abs_difference < 1.0e-10);
	/// ```
	fn cosh(self) -> Self;

	/// Hyperbolic tangent function.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let e = f64::consts::E;
	/// let x = 1.0;
	///
	/// let f = x.tanh();
	/// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
	/// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
	/// let abs_difference = (f - g).abs();
	///
	/// assert!(abs_difference < 1.0e-10);
	/// ```
	fn tanh(self) -> Self;

	/// Inverse hyperbolic sine function.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 1.0;
	/// let f = x.sinh().asinh();
	///
	/// let abs_difference = (f - x).abs();
	///
	/// assert!(abs_difference < 1.0e-10);
	/// ```
	fn asinh(self) -> Self;

	/// Inverse hyperbolic cosine function.
	///
	/// ```
	/// use num_traits::real::Real;
	///
	/// let x = 1.0;
	/// let f = x.cosh().acosh();
	///
	/// let abs_difference = (f - x).abs();
	///
	/// assert!(abs_difference < 1.0e-10);
	/// ```
	fn acosh(self) -> Self;

	/// Inverse hyperbolic tangent function.
	///
	/// ```
	/// use num_traits::real::Real;
	/// use std::f64;
	///
	/// let e = f64::consts::E;
	/// let f = e.tanh().atanh();
	///
	/// let abs_difference = (f - e).abs();
	///
	/// assert!(abs_difference < 1.0e-10);
	/// ```
	fn atanh(self) -> Self;
	}

	impl<T: Float> Real for T {
	forward! {
	Float::min_value() -> Self;
	Float::min_positive_value() -> Self;
	Float::epsilon() -> Self;
	Float::max_value() -> Self;
	}
	forward! {
	Float::floor(self) -> Self;
	Float::ceil(self) -> Self;
	Float::round(self) -> Self;
	Float::trunc(self) -> Self;
	Float::fract(self) -> Self;
	Float::abs(self) -> Self;
	Float::signum(self) -> Self;
	Float::is_sign_positive(self) -> bool;
	Float::is_sign_negative(self) -> bool;
	Float::mul_add(self, a: Self, b: Self) -> Self;
	Float::recip(self) -> Self;
	Float::powi(self, n: i32) -> Self;
	Float::powf(self, n: Self) -> Self;
	Float::sqrt(self) -> Self;
	Float::exp(self) -> Self;
	Float::exp2(self) -> Self;
	Float::ln(self) -> Self;
	Float::log(self, base: Self) -> Self;
	Float::log2(self) -> Self;
	Float::log10(self) -> Self;
	Float::to_degrees(self) -> Self;
	Float::to_radians(self) -> Self;
	Float::max(self, other: Self) -> Self;
	Float::min(self, other: Self) -> Self;
	Float::abs_sub(self, other: Self) -> Self;
	Float::cbrt(self) -> Self;
	Float::hypot(self, other: Self) -> Self;
	Float::sin(self) -> Self;
	Float::cos(self) -> Self;
	Float::tan(self) -> Self;
	Float::asin(self) -> Self;
	Float::acos(self) -> Self;
	Float::atan(self) -> Self;
	Float::atan2(self, other: Self) -> Self;
	Float::sin_cos(self) -> (Self, Self);
	Float::exp_m1(self) -> Self;
	Float::ln_1p(self) -> Self;
	Float::sinh(self) -> Self;
	Float::cosh(self) -> Self;
	Float::tanh(self) -> Self;
	Float::asinh(self) -> Self;
	Float::acosh(self) -> Self;
	Float::atanh(self) -> Self;
	}
	}