diff --git a/src/real.rs b/src/real.rs deleted file mode 100644 index f891d0f..0000000 --- a/src/real.rs +++ /dev/null @@ -1,885 +0,0 @@ -use std::ops::Neg; - -use {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. -pub trait Real: Num + Copy + NumCast + PartialOrd + Neg { - type Typo; - /// 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; - - /// Returns the real part of the float. - /// - /// ``` - /// use num_traits::Float; - /// - /// let n = 0.5f64; - /// - /// assert!(n.real() > 0.4f64); - /// ``` - fn real(self) -> Self::Typo; - - /// Returns the imaginary part of the float which equals to zero. - /// - /// ``` - /// use num_traits::Float; - /// - /// let n = 2.7f64; - /// - /// assert!(n.imag() == 0.0f64); - /// ``` - fn imag(self) -> Self::Typo; - - /// Computes the argument of the float.Float - /// - /// ``` - /// use num_traits::Float; - /// - /// let n = 0.8f32; - /// - /// assert_eq!(n.arg(), 0.0f32); - /// ``` - fn arg(self) -> Self::Typo; -} - -impl Real for T { - type Typo = T; - #[inline] - fn real(self) -> T { - self - } - #[inline] - fn imag(self) -> T { - T::neg_zero() - } - - #[inline] - fn arg(self) -> Self::Typo { - if self >= T::from(0).unwrap() { - T::from(0).unwrap() - } else { - T::from(3.14159265358979323846264338327950288_f64).unwrap() - } - } - - 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; - } -}