| use std::mem; |
| use std::ops::Neg; |
| use std::num::FpCategory; |
| |
| // Used for default implementation of `epsilon` |
| use std::f32; |
| |
| use {Num, NumCast}; |
| |
| // FIXME: these doctests aren't actually helpful, because they're using and |
| // testing the inherent methods directly, not going through `Float`. |
| |
| pub trait Float |
| : Num |
| + Copy |
| + NumCast |
| + PartialOrd |
| + Neg<Output = Self> |
| { |
| /// Returns the `NaN` value. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// let nan: f32 = Float::nan(); |
| /// |
| /// assert!(nan.is_nan()); |
| /// ``` |
| fn nan() -> Self; |
| /// Returns the infinite value. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// use std::f32; |
| /// |
| /// let infinity: f32 = Float::infinity(); |
| /// |
| /// assert!(infinity.is_infinite()); |
| /// assert!(!infinity.is_finite()); |
| /// assert!(infinity > f32::MAX); |
| /// ``` |
| fn infinity() -> Self; |
| /// Returns the negative infinite value. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// use std::f32; |
| /// |
| /// let neg_infinity: f32 = Float::neg_infinity(); |
| /// |
| /// assert!(neg_infinity.is_infinite()); |
| /// assert!(!neg_infinity.is_finite()); |
| /// assert!(neg_infinity < f32::MIN); |
| /// ``` |
| fn neg_infinity() -> Self; |
| /// Returns `-0.0`. |
| /// |
| /// ``` |
| /// use num_traits::{Zero, Float}; |
| /// |
| /// let inf: f32 = Float::infinity(); |
| /// let zero: f32 = Zero::zero(); |
| /// let neg_zero: f32 = Float::neg_zero(); |
| /// |
| /// assert_eq!(zero, neg_zero); |
| /// assert_eq!(7.0f32/inf, zero); |
| /// assert_eq!(zero * 10.0, zero); |
| /// ``` |
| fn neg_zero() -> Self; |
| |
| /// Returns the smallest finite value that this type can represent. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// use std::f64; |
| /// |
| /// let x: f64 = Float::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::Float; |
| /// use std::f64; |
| /// |
| /// let x: f64 = Float::min_positive_value(); |
| /// |
| /// assert_eq!(x, f64::MIN_POSITIVE); |
| /// ``` |
| fn min_positive_value() -> Self; |
| |
| /// Returns epsilon, a small positive value. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// use std::f64; |
| /// |
| /// let x: f64 = Float::epsilon(); |
| /// |
| /// assert_eq!(x, f64::EPSILON); |
| /// ``` |
| /// |
| /// # Panics |
| /// |
| /// The default implementation will panic if `f32::EPSILON` cannot |
| /// be cast to `Self`. |
| fn epsilon() -> Self { |
| Self::from(f32::EPSILON).expect("Unable to cast from f32::EPSILON") |
| } |
| |
| /// Returns the largest finite value that this type can represent. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// use std::f64; |
| /// |
| /// let x: f64 = Float::max_value(); |
| /// assert_eq!(x, f64::MAX); |
| /// ``` |
| fn max_value() -> Self; |
| |
| /// Returns `true` if this value is `NaN` and false otherwise. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// use std::f64; |
| /// |
| /// let nan = f64::NAN; |
| /// let f = 7.0; |
| /// |
| /// assert!(nan.is_nan()); |
| /// assert!(!f.is_nan()); |
| /// ``` |
| fn is_nan(self) -> bool; |
| |
| /// Returns `true` if this value is positive infinity or negative infinity and |
| /// false otherwise. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// use std::f32; |
| /// |
| /// let f = 7.0f32; |
| /// let inf: f32 = Float::infinity(); |
| /// let neg_inf: f32 = Float::neg_infinity(); |
| /// let nan: f32 = f32::NAN; |
| /// |
| /// assert!(!f.is_infinite()); |
| /// assert!(!nan.is_infinite()); |
| /// |
| /// assert!(inf.is_infinite()); |
| /// assert!(neg_inf.is_infinite()); |
| /// ``` |
| fn is_infinite(self) -> bool; |
| |
| /// Returns `true` if this number is neither infinite nor `NaN`. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// use std::f32; |
| /// |
| /// let f = 7.0f32; |
| /// let inf: f32 = Float::infinity(); |
| /// let neg_inf: f32 = Float::neg_infinity(); |
| /// let nan: f32 = f32::NAN; |
| /// |
| /// assert!(f.is_finite()); |
| /// |
| /// assert!(!nan.is_finite()); |
| /// assert!(!inf.is_finite()); |
| /// assert!(!neg_inf.is_finite()); |
| /// ``` |
| fn is_finite(self) -> bool; |
| |
| /// Returns `true` if the number is neither zero, infinite, |
| /// [subnormal][subnormal], or `NaN`. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// use std::f32; |
| /// |
| /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32 |
| /// let max = f32::MAX; |
| /// let lower_than_min = 1.0e-40_f32; |
| /// let zero = 0.0f32; |
| /// |
| /// assert!(min.is_normal()); |
| /// assert!(max.is_normal()); |
| /// |
| /// assert!(!zero.is_normal()); |
| /// assert!(!f32::NAN.is_normal()); |
| /// assert!(!f32::INFINITY.is_normal()); |
| /// // Values between `0` and `min` are Subnormal. |
| /// assert!(!lower_than_min.is_normal()); |
| /// ``` |
| /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number |
| fn is_normal(self) -> bool; |
| |
| /// Returns the floating point category of the number. If only one property |
| /// is going to be tested, it is generally faster to use the specific |
| /// predicate instead. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// use std::num::FpCategory; |
| /// use std::f32; |
| /// |
| /// let num = 12.4f32; |
| /// let inf = f32::INFINITY; |
| /// |
| /// assert_eq!(num.classify(), FpCategory::Normal); |
| /// assert_eq!(inf.classify(), FpCategory::Infinite); |
| /// ``` |
| fn classify(self) -> FpCategory; |
| |
| /// Returns the largest integer less than or equal to a number. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// 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!(f64::NAN.abs().is_nan()); |
| /// ``` |
| 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::Float; |
| /// 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::Float; |
| /// 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::Float; |
| /// 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. This produces a more accurate result with better performance than |
| /// a separate multiplication operation followed by an add. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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 floating point power. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// 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 number. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// let positive = 4.0; |
| /// let negative = -4.0; |
| /// |
| /// let abs_difference = (positive.sqrt() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// assert!(negative.sqrt().is_nan()); |
| /// ``` |
| fn sqrt(self) -> Self; |
| |
| /// Returns `e^(self)`, (the exponential function). |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// 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. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// 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. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// 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. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// 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); |
| /// ``` |
| #[inline] |
| fn to_degrees(self) -> Self { |
| let halfpi = Self::zero().acos(); |
| let ninety = Self::from(90u8).unwrap(); |
| self * ninety / halfpi |
| } |
| |
| /// 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); |
| /// ``` |
| #[inline] |
| fn to_radians(self) -> Self { |
| let halfpi = Self::zero().acos(); |
| let ninety = Self::from(90u8).unwrap(); |
| self * halfpi / ninety |
| } |
| |
| /// Returns the maximum of the two numbers. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// 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::Float; |
| /// 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::Float; |
| /// 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]. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// 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]. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// 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::Float; |
| /// 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::Float; |
| /// |
| /// 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. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// 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::Float; |
| /// 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::Float; |
| /// 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::Float; |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// |
| /// 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::Float; |
| /// 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 mantissa, base 2 exponent, and sign as integers, respectively. |
| /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`. |
| /// The floating point encoding is documented in the [Reference][floating-point]. |
| /// |
| /// ``` |
| /// use num_traits::Float; |
| /// |
| /// let num = 2.0f32; |
| /// |
| /// // (8388608, -22, 1) |
| /// let (mantissa, exponent, sign) = Float::integer_decode(num); |
| /// let sign_f = sign as f32; |
| /// let mantissa_f = mantissa as f32; |
| /// let exponent_f = num.powf(exponent as f32); |
| /// |
| /// // 1 * 8388608 * 2^(-22) == 2 |
| /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| /// [floating-point]: ../../../../../reference.html#machine-types |
| fn integer_decode(self) -> (u64, i16, i8); |
| } |
| |
| macro_rules! float_impl { |
| ($T:ident $decode:ident) => ( |
| impl Float for $T { |
| #[inline] |
| fn nan() -> Self { |
| ::std::$T::NAN |
| } |
| |
| #[inline] |
| fn infinity() -> Self { |
| ::std::$T::INFINITY |
| } |
| |
| #[inline] |
| fn neg_infinity() -> Self { |
| ::std::$T::NEG_INFINITY |
| } |
| |
| #[inline] |
| fn neg_zero() -> Self { |
| -0.0 |
| } |
| |
| #[inline] |
| fn min_value() -> Self { |
| ::std::$T::MIN |
| } |
| |
| #[inline] |
| fn min_positive_value() -> Self { |
| ::std::$T::MIN_POSITIVE |
| } |
| |
| #[inline] |
| fn epsilon() -> Self { |
| ::std::$T::EPSILON |
| } |
| |
| #[inline] |
| fn max_value() -> Self { |
| ::std::$T::MAX |
| } |
| |
| #[inline] |
| fn is_nan(self) -> bool { |
| <$T>::is_nan(self) |
| } |
| |
| #[inline] |
| fn is_infinite(self) -> bool { |
| <$T>::is_infinite(self) |
| } |
| |
| #[inline] |
| fn is_finite(self) -> bool { |
| <$T>::is_finite(self) |
| } |
| |
| #[inline] |
| fn is_normal(self) -> bool { |
| <$T>::is_normal(self) |
| } |
| |
| #[inline] |
| fn classify(self) -> FpCategory { |
| <$T>::classify(self) |
| } |
| |
| #[inline] |
| fn floor(self) -> Self { |
| <$T>::floor(self) |
| } |
| |
| #[inline] |
| fn ceil(self) -> Self { |
| <$T>::ceil(self) |
| } |
| |
| #[inline] |
| fn round(self) -> Self { |
| <$T>::round(self) |
| } |
| |
| #[inline] |
| fn trunc(self) -> Self { |
| <$T>::trunc(self) |
| } |
| |
| #[inline] |
| fn fract(self) -> Self { |
| <$T>::fract(self) |
| } |
| |
| #[inline] |
| fn abs(self) -> Self { |
| <$T>::abs(self) |
| } |
| |
| #[inline] |
| fn signum(self) -> Self { |
| <$T>::signum(self) |
| } |
| |
| #[inline] |
| fn is_sign_positive(self) -> bool { |
| <$T>::is_sign_positive(self) |
| } |
| |
| #[inline] |
| fn is_sign_negative(self) -> bool { |
| <$T>::is_sign_negative(self) |
| } |
| |
| #[inline] |
| fn mul_add(self, a: Self, b: Self) -> Self { |
| <$T>::mul_add(self, a, b) |
| } |
| |
| #[inline] |
| fn recip(self) -> Self { |
| <$T>::recip(self) |
| } |
| |
| #[inline] |
| fn powi(self, n: i32) -> Self { |
| <$T>::powi(self, n) |
| } |
| |
| #[inline] |
| fn powf(self, n: Self) -> Self { |
| <$T>::powf(self, n) |
| } |
| |
| #[inline] |
| fn sqrt(self) -> Self { |
| <$T>::sqrt(self) |
| } |
| |
| #[inline] |
| fn exp(self) -> Self { |
| <$T>::exp(self) |
| } |
| |
| #[inline] |
| fn exp2(self) -> Self { |
| <$T>::exp2(self) |
| } |
| |
| #[inline] |
| fn ln(self) -> Self { |
| <$T>::ln(self) |
| } |
| |
| #[inline] |
| fn log(self, base: Self) -> Self { |
| <$T>::log(self, base) |
| } |
| |
| #[inline] |
| fn log2(self) -> Self { |
| <$T>::log2(self) |
| } |
| |
| #[inline] |
| fn log10(self) -> Self { |
| <$T>::log10(self) |
| } |
| |
| #[inline] |
| fn to_degrees(self) -> Self { |
| // NB: `f32` didn't stabilize this until 1.7 |
| // <$T>::to_degrees(self) |
| self * (180. / ::std::$T::consts::PI) |
| } |
| |
| #[inline] |
| fn to_radians(self) -> Self { |
| // NB: `f32` didn't stabilize this until 1.7 |
| // <$T>::to_radians(self) |
| self * (::std::$T::consts::PI / 180.) |
| } |
| |
| #[inline] |
| fn max(self, other: Self) -> Self { |
| <$T>::max(self, other) |
| } |
| |
| #[inline] |
| fn min(self, other: Self) -> Self { |
| <$T>::min(self, other) |
| } |
| |
| #[inline] |
| #[allow(deprecated)] |
| fn abs_sub(self, other: Self) -> Self { |
| <$T>::abs_sub(self, other) |
| } |
| |
| #[inline] |
| fn cbrt(self) -> Self { |
| <$T>::cbrt(self) |
| } |
| |
| #[inline] |
| fn hypot(self, other: Self) -> Self { |
| <$T>::hypot(self, other) |
| } |
| |
| #[inline] |
| fn sin(self) -> Self { |
| <$T>::sin(self) |
| } |
| |
| #[inline] |
| fn cos(self) -> Self { |
| <$T>::cos(self) |
| } |
| |
| #[inline] |
| fn tan(self) -> Self { |
| <$T>::tan(self) |
| } |
| |
| #[inline] |
| fn asin(self) -> Self { |
| <$T>::asin(self) |
| } |
| |
| #[inline] |
| fn acos(self) -> Self { |
| <$T>::acos(self) |
| } |
| |
| #[inline] |
| fn atan(self) -> Self { |
| <$T>::atan(self) |
| } |
| |
| #[inline] |
| fn atan2(self, other: Self) -> Self { |
| <$T>::atan2(self, other) |
| } |
| |
| #[inline] |
| fn sin_cos(self) -> (Self, Self) { |
| <$T>::sin_cos(self) |
| } |
| |
| #[inline] |
| fn exp_m1(self) -> Self { |
| <$T>::exp_m1(self) |
| } |
| |
| #[inline] |
| fn ln_1p(self) -> Self { |
| <$T>::ln_1p(self) |
| } |
| |
| #[inline] |
| fn sinh(self) -> Self { |
| <$T>::sinh(self) |
| } |
| |
| #[inline] |
| fn cosh(self) -> Self { |
| <$T>::cosh(self) |
| } |
| |
| #[inline] |
| fn tanh(self) -> Self { |
| <$T>::tanh(self) |
| } |
| |
| #[inline] |
| fn asinh(self) -> Self { |
| <$T>::asinh(self) |
| } |
| |
| #[inline] |
| fn acosh(self) -> Self { |
| <$T>::acosh(self) |
| } |
| |
| #[inline] |
| fn atanh(self) -> Self { |
| <$T>::atanh(self) |
| } |
| |
| #[inline] |
| fn integer_decode(self) -> (u64, i16, i8) { |
| $decode(self) |
| } |
| } |
| ) |
| } |
| |
| fn integer_decode_f32(f: f32) -> (u64, i16, i8) { |
| let bits: u32 = unsafe { mem::transmute(f) }; |
| let sign: i8 = if bits >> 31 == 0 { |
| 1 |
| } else { |
| -1 |
| }; |
| let mut exponent: i16 = ((bits >> 23) & 0xff) as i16; |
| let mantissa = if exponent == 0 { |
| (bits & 0x7fffff) << 1 |
| } else { |
| (bits & 0x7fffff) | 0x800000 |
| }; |
| // Exponent bias + mantissa shift |
| exponent -= 127 + 23; |
| (mantissa as u64, exponent, sign) |
| } |
| |
| fn integer_decode_f64(f: f64) -> (u64, i16, i8) { |
| let bits: u64 = unsafe { mem::transmute(f) }; |
| let sign: i8 = if bits >> 63 == 0 { |
| 1 |
| } else { |
| -1 |
| }; |
| let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16; |
| let mantissa = if exponent == 0 { |
| (bits & 0xfffffffffffff) << 1 |
| } else { |
| (bits & 0xfffffffffffff) | 0x10000000000000 |
| }; |
| // Exponent bias + mantissa shift |
| exponent -= 1023 + 52; |
| (mantissa, exponent, sign) |
| } |
| |
| float_impl!(f32 integer_decode_f32); |
| float_impl!(f64 integer_decode_f64); |
| |
| macro_rules! float_const_impl { |
| ($(#[$doc:meta] $constant:ident,)+) => ( |
| #[allow(non_snake_case)] |
| pub trait FloatConst { |
| $(#[$doc] fn $constant() -> Self;)+ |
| } |
| float_const_impl! { @float f32, $($constant,)+ } |
| float_const_impl! { @float f64, $($constant,)+ } |
| ); |
| (@float $T:ident, $($constant:ident,)+) => ( |
| impl FloatConst for $T { |
| $( |
| #[inline] |
| fn $constant() -> Self { |
| ::std::$T::consts::$constant |
| } |
| )+ |
| } |
| ); |
| } |
| |
| float_const_impl! { |
| #[doc = "Return Euler’s number."] |
| E, |
| #[doc = "Return `1.0 / π`."] |
| FRAC_1_PI, |
| #[doc = "Return `1.0 / sqrt(2.0)`."] |
| FRAC_1_SQRT_2, |
| #[doc = "Return `2.0 / π`."] |
| FRAC_2_PI, |
| #[doc = "Return `2.0 / sqrt(π)`."] |
| FRAC_2_SQRT_PI, |
| #[doc = "Return `π / 2.0`."] |
| FRAC_PI_2, |
| #[doc = "Return `π / 3.0`."] |
| FRAC_PI_3, |
| #[doc = "Return `π / 4.0`."] |
| FRAC_PI_4, |
| #[doc = "Return `π / 6.0`."] |
| FRAC_PI_6, |
| #[doc = "Return `π / 8.0`."] |
| FRAC_PI_8, |
| #[doc = "Return `ln(10.0)`."] |
| LN_10, |
| #[doc = "Return `ln(2.0)`."] |
| LN_2, |
| #[doc = "Return `log10(e)`."] |
| LOG10_E, |
| #[doc = "Return `log2(e)`."] |
| LOG2_E, |
| #[doc = "Return Archimedes’ constant."] |
| PI, |
| #[doc = "Return `sqrt(2.0)`."] |
| SQRT_2, |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| use Float; |
| |
| #[test] |
| fn convert_deg_rad() { |
| use std::f64::consts; |
| |
| const DEG_RAD_PAIRS: [(f64, f64); 7] = [ |
| (0.0, 0.), |
| (22.5, consts::FRAC_PI_8), |
| (30.0, consts::FRAC_PI_6), |
| (45.0, consts::FRAC_PI_4), |
| (60.0, consts::FRAC_PI_3), |
| (90.0, consts::FRAC_PI_2), |
| (180.0, consts::PI), |
| ]; |
| |
| for &(deg, rad) in &DEG_RAD_PAIRS { |
| assert!((Float::to_degrees(rad) - deg).abs() < 1e-6); |
| assert!((Float::to_radians(deg) - rad).abs() < 1e-6); |
| |
| let (deg, rad) = (deg as f32, rad as f32); |
| assert!((Float::to_degrees(rad) - deg).abs() < 1e-6); |
| assert!((Float::to_radians(deg) - rad).abs() < 1e-6); |
| } |
| } |
| } |
