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Diffstat (limited to 'vendor/num-traits/src/real.rs')
| -rw-r--r-- | vendor/num-traits/src/real.rs | 834 |
1 files changed, 834 insertions, 0 deletions
diff --git a/vendor/num-traits/src/real.rs b/vendor/num-traits/src/real.rs new file mode 100644 index 0000000..d4feee0 --- /dev/null +++ b/vendor/num-traits/src/real.rs @@ -0,0 +1,834 @@ +#![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; + } +} |