diff options
Diffstat (limited to 'vendor/num-traits/src/float.rs')
| -rw-r--r-- | vendor/num-traits/src/float.rs | 2344 |
1 files changed, 0 insertions, 2344 deletions
diff --git a/vendor/num-traits/src/float.rs b/vendor/num-traits/src/float.rs deleted file mode 100644 index 87f8387..0000000 --- a/vendor/num-traits/src/float.rs +++ /dev/null @@ -1,2344 +0,0 @@ -use core::num::FpCategory; -use core::ops::{Add, Div, Neg}; - -use core::f32; -use core::f64; - -use crate::{Num, NumCast, ToPrimitive}; - -/// Generic trait for floating point numbers that works with `no_std`. -/// -/// This trait implements a subset of the `Float` trait. -pub trait FloatCore: Num + NumCast + Neg<Output = Self> + PartialOrd + Copy { - /// Returns positive infinity. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T) { - /// assert!(T::infinity() == x); - /// } - /// - /// check(f32::INFINITY); - /// check(f64::INFINITY); - /// ``` - fn infinity() -> Self; - - /// Returns negative infinity. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T) { - /// assert!(T::neg_infinity() == x); - /// } - /// - /// check(f32::NEG_INFINITY); - /// check(f64::NEG_INFINITY); - /// ``` - fn neg_infinity() -> Self; - - /// Returns NaN. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// - /// fn check<T: FloatCore>() { - /// let n = T::nan(); - /// assert!(n != n); - /// } - /// - /// check::<f32>(); - /// check::<f64>(); - /// ``` - fn nan() -> Self; - - /// Returns `-0.0`. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(n: T) { - /// let z = T::neg_zero(); - /// assert!(z.is_zero()); - /// assert!(T::one() / z == n); - /// } - /// - /// check(f32::NEG_INFINITY); - /// check(f64::NEG_INFINITY); - /// ``` - fn neg_zero() -> Self; - - /// Returns the smallest finite value that this type can represent. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T) { - /// assert!(T::min_value() == x); - /// } - /// - /// check(f32::MIN); - /// check(f64::MIN); - /// ``` - fn min_value() -> Self; - - /// Returns the smallest positive, normalized value that this type can represent. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T) { - /// assert!(T::min_positive_value() == x); - /// } - /// - /// check(f32::MIN_POSITIVE); - /// check(f64::MIN_POSITIVE); - /// ``` - fn min_positive_value() -> Self; - - /// Returns epsilon, a small positive value. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T) { - /// assert!(T::epsilon() == x); - /// } - /// - /// check(f32::EPSILON); - /// check(f64::EPSILON); - /// ``` - fn epsilon() -> Self; - - /// Returns the largest finite value that this type can represent. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T) { - /// assert!(T::max_value() == x); - /// } - /// - /// check(f32::MAX); - /// check(f64::MAX); - /// ``` - fn max_value() -> Self; - - /// Returns `true` if the number is NaN. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, p: bool) { - /// assert!(x.is_nan() == p); - /// } - /// - /// check(f32::NAN, true); - /// check(f32::INFINITY, false); - /// check(f64::NAN, true); - /// check(0.0f64, false); - /// ``` - #[inline] - #[allow(clippy::eq_op)] - fn is_nan(self) -> bool { - self != self - } - - /// Returns `true` if the number is infinite. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, p: bool) { - /// assert!(x.is_infinite() == p); - /// } - /// - /// check(f32::INFINITY, true); - /// check(f32::NEG_INFINITY, true); - /// check(f32::NAN, false); - /// check(f64::INFINITY, true); - /// check(f64::NEG_INFINITY, true); - /// check(0.0f64, false); - /// ``` - #[inline] - fn is_infinite(self) -> bool { - self == Self::infinity() || self == Self::neg_infinity() - } - - /// Returns `true` if the number is neither infinite or NaN. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, p: bool) { - /// assert!(x.is_finite() == p); - /// } - /// - /// check(f32::INFINITY, false); - /// check(f32::MAX, true); - /// check(f64::NEG_INFINITY, false); - /// check(f64::MIN_POSITIVE, true); - /// check(f64::NAN, false); - /// ``` - #[inline] - fn is_finite(self) -> bool { - !(self.is_nan() || self.is_infinite()) - } - - /// Returns `true` if the number is neither zero, infinite, subnormal or NaN. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, p: bool) { - /// assert!(x.is_normal() == p); - /// } - /// - /// check(f32::INFINITY, false); - /// check(f32::MAX, true); - /// check(f64::NEG_INFINITY, false); - /// check(f64::MIN_POSITIVE, true); - /// check(0.0f64, false); - /// ``` - #[inline] - fn is_normal(self) -> bool { - self.classify() == FpCategory::Normal - } - - /// Returns `true` if the number is [subnormal]. - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::f64; - /// - /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64 - /// let max = f64::MAX; - /// let lower_than_min = 1.0e-308_f64; - /// let zero = 0.0_f64; - /// - /// assert!(!min.is_subnormal()); - /// assert!(!max.is_subnormal()); - /// - /// assert!(!zero.is_subnormal()); - /// assert!(!f64::NAN.is_subnormal()); - /// assert!(!f64::INFINITY.is_subnormal()); - /// // Values between `0` and `min` are Subnormal. - /// assert!(lower_than_min.is_subnormal()); - /// ``` - /// [subnormal]: https://en.wikipedia.org/wiki/Subnormal_number - #[inline] - fn is_subnormal(self) -> bool { - self.classify() == FpCategory::Subnormal - } - - /// 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. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// use std::num::FpCategory; - /// - /// fn check<T: FloatCore>(x: T, c: FpCategory) { - /// assert!(x.classify() == c); - /// } - /// - /// check(f32::INFINITY, FpCategory::Infinite); - /// check(f32::MAX, FpCategory::Normal); - /// check(f64::NAN, FpCategory::Nan); - /// check(f64::MIN_POSITIVE, FpCategory::Normal); - /// check(f64::MIN_POSITIVE / 2.0, FpCategory::Subnormal); - /// check(0.0f64, FpCategory::Zero); - /// ``` - fn classify(self) -> FpCategory; - - /// Returns the largest integer less than or equal to a number. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, y: T) { - /// assert!(x.floor() == y); - /// } - /// - /// check(f32::INFINITY, f32::INFINITY); - /// check(0.9f32, 0.0); - /// check(1.0f32, 1.0); - /// check(1.1f32, 1.0); - /// check(-0.0f64, 0.0); - /// check(-0.9f64, -1.0); - /// check(-1.0f64, -1.0); - /// check(-1.1f64, -2.0); - /// check(f64::MIN, f64::MIN); - /// ``` - #[inline] - fn floor(self) -> Self { - let f = self.fract(); - if f.is_nan() || f.is_zero() { - self - } else if self < Self::zero() { - self - f - Self::one() - } else { - self - f - } - } - - /// Returns the smallest integer greater than or equal to a number. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, y: T) { - /// assert!(x.ceil() == y); - /// } - /// - /// check(f32::INFINITY, f32::INFINITY); - /// check(0.9f32, 1.0); - /// check(1.0f32, 1.0); - /// check(1.1f32, 2.0); - /// check(-0.0f64, 0.0); - /// check(-0.9f64, -0.0); - /// check(-1.0f64, -1.0); - /// check(-1.1f64, -1.0); - /// check(f64::MIN, f64::MIN); - /// ``` - #[inline] - fn ceil(self) -> Self { - let f = self.fract(); - if f.is_nan() || f.is_zero() { - self - } else if self > Self::zero() { - self - f + Self::one() - } else { - self - f - } - } - - /// Returns the nearest integer to a number. Round half-way cases away from `0.0`. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, y: T) { - /// assert!(x.round() == y); - /// } - /// - /// check(f32::INFINITY, f32::INFINITY); - /// check(0.4f32, 0.0); - /// check(0.5f32, 1.0); - /// check(0.6f32, 1.0); - /// check(-0.4f64, 0.0); - /// check(-0.5f64, -1.0); - /// check(-0.6f64, -1.0); - /// check(f64::MIN, f64::MIN); - /// ``` - #[inline] - fn round(self) -> Self { - let one = Self::one(); - let h = Self::from(0.5).expect("Unable to cast from 0.5"); - let f = self.fract(); - if f.is_nan() || f.is_zero() { - self - } else if self > Self::zero() { - if f < h { - self - f - } else { - self - f + one - } - } else if -f < h { - self - f - } else { - self - f - one - } - } - - /// Return the integer part of a number. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, y: T) { - /// assert!(x.trunc() == y); - /// } - /// - /// check(f32::INFINITY, f32::INFINITY); - /// check(0.9f32, 0.0); - /// check(1.0f32, 1.0); - /// check(1.1f32, 1.0); - /// check(-0.0f64, 0.0); - /// check(-0.9f64, -0.0); - /// check(-1.0f64, -1.0); - /// check(-1.1f64, -1.0); - /// check(f64::MIN, f64::MIN); - /// ``` - #[inline] - fn trunc(self) -> Self { - let f = self.fract(); - if f.is_nan() { - self - } else { - self - f - } - } - - /// Returns the fractional part of a number. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, y: T) { - /// assert!(x.fract() == y); - /// } - /// - /// check(f32::MAX, 0.0); - /// check(0.75f32, 0.75); - /// check(1.0f32, 0.0); - /// check(1.25f32, 0.25); - /// check(-0.0f64, 0.0); - /// check(-0.75f64, -0.75); - /// check(-1.0f64, 0.0); - /// check(-1.25f64, -0.25); - /// check(f64::MIN, 0.0); - /// ``` - #[inline] - fn fract(self) -> Self { - if self.is_zero() { - Self::zero() - } else { - self % Self::one() - } - } - - /// Computes the absolute value of `self`. Returns `FloatCore::nan()` if the - /// number is `FloatCore::nan()`. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, y: T) { - /// assert!(x.abs() == y); - /// } - /// - /// check(f32::INFINITY, f32::INFINITY); - /// check(1.0f32, 1.0); - /// check(0.0f64, 0.0); - /// check(-0.0f64, 0.0); - /// check(-1.0f64, 1.0); - /// check(f64::MIN, f64::MAX); - /// ``` - #[inline] - fn abs(self) -> Self { - if self.is_sign_positive() { - return self; - } - if self.is_sign_negative() { - return -self; - } - Self::nan() - } - - /// Returns a number that represents the sign of `self`. - /// - /// - `1.0` if the number is positive, `+0.0` or `FloatCore::infinity()` - /// - `-1.0` if the number is negative, `-0.0` or `FloatCore::neg_infinity()` - /// - `FloatCore::nan()` if the number is `FloatCore::nan()` - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, y: T) { - /// assert!(x.signum() == y); - /// } - /// - /// check(f32::INFINITY, 1.0); - /// check(3.0f32, 1.0); - /// check(0.0f32, 1.0); - /// check(-0.0f64, -1.0); - /// check(-3.0f64, -1.0); - /// check(f64::MIN, -1.0); - /// ``` - #[inline] - fn signum(self) -> Self { - if self.is_nan() { - Self::nan() - } else if self.is_sign_negative() { - -Self::one() - } else { - Self::one() - } - } - - /// Returns `true` if `self` is positive, including `+0.0` and - /// `FloatCore::infinity()`, and `FloatCore::nan()`. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, p: bool) { - /// assert!(x.is_sign_positive() == p); - /// } - /// - /// check(f32::INFINITY, true); - /// check(f32::MAX, true); - /// check(0.0f32, true); - /// check(-0.0f64, false); - /// check(f64::NEG_INFINITY, false); - /// check(f64::MIN_POSITIVE, true); - /// check(f64::NAN, true); - /// check(-f64::NAN, false); - /// ``` - #[inline] - fn is_sign_positive(self) -> bool { - !self.is_sign_negative() - } - - /// Returns `true` if `self` is negative, including `-0.0` and - /// `FloatCore::neg_infinity()`, and `-FloatCore::nan()`. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, p: bool) { - /// assert!(x.is_sign_negative() == p); - /// } - /// - /// check(f32::INFINITY, false); - /// check(f32::MAX, false); - /// check(0.0f32, false); - /// check(-0.0f64, true); - /// check(f64::NEG_INFINITY, true); - /// check(f64::MIN_POSITIVE, false); - /// check(f64::NAN, false); - /// check(-f64::NAN, true); - /// ``` - #[inline] - fn is_sign_negative(self) -> bool { - let (_, _, sign) = self.integer_decode(); - sign < 0 - } - - /// Returns the minimum of the two numbers. - /// - /// If one of the arguments is NaN, then the other argument is returned. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, y: T, min: T) { - /// assert!(x.min(y) == min); - /// } - /// - /// check(1.0f32, 2.0, 1.0); - /// check(f32::NAN, 2.0, 2.0); - /// check(1.0f64, -2.0, -2.0); - /// check(1.0f64, f64::NAN, 1.0); - /// ``` - #[inline] - fn min(self, other: Self) -> Self { - if self.is_nan() { - return other; - } - if other.is_nan() { - return self; - } - if self < other { - self - } else { - other - } - } - - /// Returns the maximum of the two numbers. - /// - /// If one of the arguments is NaN, then the other argument is returned. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, y: T, max: T) { - /// assert!(x.max(y) == max); - /// } - /// - /// check(1.0f32, 2.0, 2.0); - /// check(1.0f32, f32::NAN, 1.0); - /// check(-1.0f64, 2.0, 2.0); - /// check(-1.0f64, f64::NAN, -1.0); - /// ``` - #[inline] - fn max(self, other: Self) -> Self { - if self.is_nan() { - return other; - } - if other.is_nan() { - return self; - } - if self > other { - self - } else { - other - } - } - - /// Returns the reciprocal (multiplicative inverse) of the number. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, y: T) { - /// assert!(x.recip() == y); - /// assert!(y.recip() == x); - /// } - /// - /// check(f32::INFINITY, 0.0); - /// check(2.0f32, 0.5); - /// check(-0.25f64, -4.0); - /// check(-0.0f64, f64::NEG_INFINITY); - /// ``` - #[inline] - fn recip(self) -> Self { - Self::one() / self - } - - /// Raise a number to an integer power. - /// - /// Using this function is generally faster than using `powf` - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// - /// fn check<T: FloatCore>(x: T, exp: i32, powi: T) { - /// assert!(x.powi(exp) == powi); - /// } - /// - /// check(9.0f32, 2, 81.0); - /// check(1.0f32, -2, 1.0); - /// check(10.0f64, 20, 1e20); - /// check(4.0f64, -2, 0.0625); - /// check(-1.0f64, std::i32::MIN, 1.0); - /// ``` - #[inline] - fn powi(mut self, mut exp: i32) -> Self { - if exp < 0 { - exp = exp.wrapping_neg(); - self = self.recip(); - } - // It should always be possible to convert a positive `i32` to a `usize`. - // Note, `i32::MIN` will wrap and still be negative, so we need to convert - // to `u32` without sign-extension before growing to `usize`. - super::pow(self, (exp as u32).to_usize().unwrap()) - } - - /// Converts to degrees, assuming the number is in radians. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(rad: T, deg: T) { - /// assert!(rad.to_degrees() == deg); - /// } - /// - /// check(0.0f32, 0.0); - /// check(f32::consts::PI, 180.0); - /// check(f64::consts::FRAC_PI_4, 45.0); - /// check(f64::INFINITY, f64::INFINITY); - /// ``` - fn to_degrees(self) -> Self; - - /// Converts to radians, assuming the number is in degrees. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(deg: T, rad: T) { - /// assert!(deg.to_radians() == rad); - /// } - /// - /// check(0.0f32, 0.0); - /// check(180.0, f32::consts::PI); - /// check(45.0, f64::consts::FRAC_PI_4); - /// check(f64::INFINITY, f64::INFINITY); - /// ``` - fn to_radians(self) -> Self; - - /// Returns the mantissa, base 2 exponent, and sign as integers, respectively. - /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`. - /// - /// # Examples - /// - /// ``` - /// use num_traits::float::FloatCore; - /// use std::{f32, f64}; - /// - /// fn check<T: FloatCore>(x: T, m: u64, e: i16, s:i8) { - /// let (mantissa, exponent, sign) = x.integer_decode(); - /// assert_eq!(mantissa, m); - /// assert_eq!(exponent, e); - /// assert_eq!(sign, s); - /// } - /// - /// check(2.0f32, 1 << 23, -22, 1); - /// check(-2.0f32, 1 << 23, -22, -1); - /// check(f32::INFINITY, 1 << 23, 105, 1); - /// check(f64::NEG_INFINITY, 1 << 52, 972, -1); - /// ``` - fn integer_decode(self) -> (u64, i16, i8); -} - -impl FloatCore for f32 { - constant! { - infinity() -> f32::INFINITY; - neg_infinity() -> f32::NEG_INFINITY; - nan() -> f32::NAN; - neg_zero() -> -0.0; - min_value() -> f32::MIN; - min_positive_value() -> f32::MIN_POSITIVE; - epsilon() -> f32::EPSILON; - max_value() -> f32::MAX; - } - - #[inline] - fn integer_decode(self) -> (u64, i16, i8) { - integer_decode_f32(self) - } - - forward! { - Self::is_nan(self) -> bool; - Self::is_infinite(self) -> bool; - Self::is_finite(self) -> bool; - Self::is_normal(self) -> bool; - Self::classify(self) -> FpCategory; - Self::is_sign_positive(self) -> bool; - Self::is_sign_negative(self) -> bool; - Self::min(self, other: Self) -> Self; - Self::max(self, other: Self) -> Self; - Self::recip(self) -> Self; - Self::to_degrees(self) -> Self; - Self::to_radians(self) -> Self; - } - - #[cfg(has_is_subnormal)] - forward! { - Self::is_subnormal(self) -> bool; - } - - #[cfg(feature = "std")] - forward! { - Self::floor(self) -> Self; - Self::ceil(self) -> Self; - Self::round(self) -> Self; - Self::trunc(self) -> Self; - Self::fract(self) -> Self; - Self::abs(self) -> Self; - Self::signum(self) -> Self; - Self::powi(self, n: i32) -> Self; - } - - #[cfg(all(not(feature = "std"), feature = "libm"))] - forward! { - libm::floorf as floor(self) -> Self; - libm::ceilf as ceil(self) -> Self; - libm::roundf as round(self) -> Self; - libm::truncf as trunc(self) -> Self; - libm::fabsf as abs(self) -> Self; - } - - #[cfg(all(not(feature = "std"), feature = "libm"))] - #[inline] - fn fract(self) -> Self { - self - libm::truncf(self) - } -} - -impl FloatCore for f64 { - constant! { - infinity() -> f64::INFINITY; - neg_infinity() -> f64::NEG_INFINITY; - nan() -> f64::NAN; - neg_zero() -> -0.0; - min_value() -> f64::MIN; - min_positive_value() -> f64::MIN_POSITIVE; - epsilon() -> f64::EPSILON; - max_value() -> f64::MAX; - } - - #[inline] - fn integer_decode(self) -> (u64, i16, i8) { - integer_decode_f64(self) - } - - forward! { - Self::is_nan(self) -> bool; - Self::is_infinite(self) -> bool; - Self::is_finite(self) -> bool; - Self::is_normal(self) -> bool; - Self::classify(self) -> FpCategory; - Self::is_sign_positive(self) -> bool; - Self::is_sign_negative(self) -> bool; - Self::min(self, other: Self) -> Self; - Self::max(self, other: Self) -> Self; - Self::recip(self) -> Self; - Self::to_degrees(self) -> Self; - Self::to_radians(self) -> Self; - } - - #[cfg(has_is_subnormal)] - forward! { - Self::is_subnormal(self) -> bool; - } - - #[cfg(feature = "std")] - forward! { - Self::floor(self) -> Self; - Self::ceil(self) -> Self; - Self::round(self) -> Self; - Self::trunc(self) -> Self; - Self::fract(self) -> Self; - Self::abs(self) -> Self; - Self::signum(self) -> Self; - Self::powi(self, n: i32) -> Self; - } - - #[cfg(all(not(feature = "std"), feature = "libm"))] - forward! { - libm::floor as floor(self) -> Self; - libm::ceil as ceil(self) -> Self; - libm::round as round(self) -> Self; - libm::trunc as trunc(self) -> Self; - libm::fabs as abs(self) -> Self; - } - - #[cfg(all(not(feature = "std"), feature = "libm"))] - #[inline] - fn fract(self) -> Self { - self - libm::trunc(self) - } -} - -// FIXME: these doctests aren't actually helpful, because they're using and -// testing the inherent methods directly, not going through `Float`. - -/// Generic trait for floating point numbers -/// -/// This trait is only available with the `std` feature, or with the `libm` feature otherwise. -#[cfg(any(feature = "std", feature = "libm"))] -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/Subnormal_number - fn is_normal(self) -> bool; - - /// Returns `true` if the number is [subnormal]. - /// - /// ``` - /// use num_traits::Float; - /// use std::f64; - /// - /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64 - /// let max = f64::MAX; - /// let lower_than_min = 1.0e-308_f64; - /// let zero = 0.0_f64; - /// - /// assert!(!min.is_subnormal()); - /// assert!(!max.is_subnormal()); - /// - /// assert!(!zero.is_subnormal()); - /// assert!(!f64::NAN.is_subnormal()); - /// assert!(!f64::INFINITY.is_subnormal()); - /// // Values between `0` and `min` are Subnormal. - /// assert!(lower_than_min.is_subnormal()); - /// ``` - /// [subnormal]: https://en.wikipedia.org/wiki/Subnormal_number - #[inline] - fn is_subnormal(self) -> bool { - self.classify() == FpCategory::Subnormal - } - - /// 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 `Float::nan()`. - /// - /// ``` - /// use num_traits::Float; - /// use std::f64; - /// - /// let nan: f64 = f64::NAN; - /// 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!(nan.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 `-Float::nan()`. - /// - /// ``` - /// use num_traits::Float; - /// use std::f64; - /// - /// let nan: f64 = f64::NAN; - /// let neg_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()); - /// assert!(neg_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::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`. - /// - /// ``` - /// 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); - /// ``` - fn integer_decode(self) -> (u64, i16, i8); - - /// Returns a number composed of the magnitude of `self` and the sign of - /// `sign`. - /// - /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise - /// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of - /// `sign` is returned. - /// - /// # Examples - /// - /// ``` - /// use num_traits::Float; - /// - /// let f = 3.5_f32; - /// - /// assert_eq!(f.copysign(0.42), 3.5_f32); - /// assert_eq!(f.copysign(-0.42), -3.5_f32); - /// assert_eq!((-f).copysign(0.42), 3.5_f32); - /// assert_eq!((-f).copysign(-0.42), -3.5_f32); - /// - /// assert!(f32::nan().copysign(1.0).is_nan()); - /// ``` - fn copysign(self, sign: Self) -> Self { - if self.is_sign_negative() == sign.is_sign_negative() { - self - } else { - self.neg() - } - } -} - -#[cfg(feature = "std")] -macro_rules! float_impl_std { - ($T:ident $decode:ident) => { - impl Float for $T { - constant! { - nan() -> $T::NAN; - infinity() -> $T::INFINITY; - neg_infinity() -> $T::NEG_INFINITY; - neg_zero() -> -0.0; - min_value() -> $T::MIN; - min_positive_value() -> $T::MIN_POSITIVE; - epsilon() -> $T::EPSILON; - max_value() -> $T::MAX; - } - - #[inline] - #[allow(deprecated)] - fn abs_sub(self, other: Self) -> Self { - <$T>::abs_sub(self, other) - } - - #[inline] - fn integer_decode(self) -> (u64, i16, i8) { - $decode(self) - } - - forward! { - Self::is_nan(self) -> bool; - Self::is_infinite(self) -> bool; - Self::is_finite(self) -> bool; - Self::is_normal(self) -> bool; - Self::classify(self) -> FpCategory; - Self::floor(self) -> Self; - Self::ceil(self) -> Self; - Self::round(self) -> Self; - Self::trunc(self) -> Self; - Self::fract(self) -> Self; - Self::abs(self) -> Self; - Self::signum(self) -> Self; - Self::is_sign_positive(self) -> bool; - Self::is_sign_negative(self) -> bool; - Self::mul_add(self, a: Self, b: Self) -> Self; - Self::recip(self) -> Self; - Self::powi(self, n: i32) -> Self; - Self::powf(self, n: Self) -> Self; - Self::sqrt(self) -> Self; - Self::exp(self) -> Self; - Self::exp2(self) -> Self; - Self::ln(self) -> Self; - Self::log(self, base: Self) -> Self; - Self::log2(self) -> Self; - Self::log10(self) -> Self; - Self::to_degrees(self) -> Self; - Self::to_radians(self) -> Self; - Self::max(self, other: Self) -> Self; - Self::min(self, other: Self) -> Self; - Self::cbrt(self) -> Self; - Self::hypot(self, other: Self) -> Self; - Self::sin(self) -> Self; - Self::cos(self) -> Self; - Self::tan(self) -> Self; - Self::asin(self) -> Self; - Self::acos(self) -> Self; - Self::atan(self) -> Self; - Self::atan2(self, other: Self) -> Self; - Self::sin_cos(self) -> (Self, Self); - Self::exp_m1(self) -> Self; - Self::ln_1p(self) -> Self; - Self::sinh(self) -> Self; - Self::cosh(self) -> Self; - Self::tanh(self) -> Self; - Self::asinh(self) -> Self; - Self::acosh(self) -> Self; - Self::atanh(self) -> Self; - } - - #[cfg(has_copysign)] - forward! { - Self::copysign(self, sign: Self) -> Self; - } - - #[cfg(has_is_subnormal)] - forward! { - Self::is_subnormal(self) -> bool; - } - } - }; -} - -#[cfg(all(not(feature = "std"), feature = "libm"))] -macro_rules! float_impl_libm { - ($T:ident $decode:ident) => { - constant! { - nan() -> $T::NAN; - infinity() -> $T::INFINITY; - neg_infinity() -> $T::NEG_INFINITY; - neg_zero() -> -0.0; - min_value() -> $T::MIN; - min_positive_value() -> $T::MIN_POSITIVE; - epsilon() -> $T::EPSILON; - max_value() -> $T::MAX; - } - - #[inline] - fn integer_decode(self) -> (u64, i16, i8) { - $decode(self) - } - - #[inline] - fn fract(self) -> Self { - self - Float::trunc(self) - } - - #[inline] - fn log(self, base: Self) -> Self { - self.ln() / base.ln() - } - - forward! { - Self::is_nan(self) -> bool; - Self::is_infinite(self) -> bool; - Self::is_finite(self) -> bool; - Self::is_normal(self) -> bool; - Self::classify(self) -> FpCategory; - Self::is_sign_positive(self) -> bool; - Self::is_sign_negative(self) -> bool; - Self::min(self, other: Self) -> Self; - Self::max(self, other: Self) -> Self; - Self::recip(self) -> Self; - Self::to_degrees(self) -> Self; - Self::to_radians(self) -> Self; - } - - #[cfg(has_is_subnormal)] - forward! { - Self::is_subnormal(self) -> bool; - } - - forward! { - FloatCore::signum(self) -> Self; - FloatCore::powi(self, n: i32) -> Self; - } - }; -} - -fn integer_decode_f32(f: f32) -> (u64, i16, i8) { - let bits: u32 = f.to_bits(); - 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 = f.to_bits(); - 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) -} - -#[cfg(feature = "std")] -float_impl_std!(f32 integer_decode_f32); -#[cfg(feature = "std")] -float_impl_std!(f64 integer_decode_f64); - -#[cfg(all(not(feature = "std"), feature = "libm"))] -impl Float for f32 { - float_impl_libm!(f32 integer_decode_f32); - - #[inline] - #[allow(deprecated)] - fn abs_sub(self, other: Self) -> Self { - libm::fdimf(self, other) - } - - forward! { - libm::floorf as floor(self) -> Self; - libm::ceilf as ceil(self) -> Self; - libm::roundf as round(self) -> Self; - libm::truncf as trunc(self) -> Self; - libm::fabsf as abs(self) -> Self; - libm::fmaf as mul_add(self, a: Self, b: Self) -> Self; - libm::powf as powf(self, n: Self) -> Self; - libm::sqrtf as sqrt(self) -> Self; - libm::expf as exp(self) -> Self; - libm::exp2f as exp2(self) -> Self; - libm::logf as ln(self) -> Self; - libm::log2f as log2(self) -> Self; - libm::log10f as log10(self) -> Self; - libm::cbrtf as cbrt(self) -> Self; - libm::hypotf as hypot(self, other: Self) -> Self; - libm::sinf as sin(self) -> Self; - libm::cosf as cos(self) -> Self; - libm::tanf as tan(self) -> Self; - libm::asinf as asin(self) -> Self; - libm::acosf as acos(self) -> Self; - libm::atanf as atan(self) -> Self; - libm::atan2f as atan2(self, other: Self) -> Self; - libm::sincosf as sin_cos(self) -> (Self, Self); - libm::expm1f as exp_m1(self) -> Self; - libm::log1pf as ln_1p(self) -> Self; - libm::sinhf as sinh(self) -> Self; - libm::coshf as cosh(self) -> Self; - libm::tanhf as tanh(self) -> Self; - libm::asinhf as asinh(self) -> Self; - libm::acoshf as acosh(self) -> Self; - libm::atanhf as atanh(self) -> Self; - libm::copysignf as copysign(self, other: Self) -> Self; - } -} - -#[cfg(all(not(feature = "std"), feature = "libm"))] -impl Float for f64 { - float_impl_libm!(f64 integer_decode_f64); - - #[inline] - #[allow(deprecated)] - fn abs_sub(self, other: Self) -> Self { - libm::fdim(self, other) - } - - forward! { - libm::floor as floor(self) -> Self; - libm::ceil as ceil(self) -> Self; - libm::round as round(self) -> Self; - libm::trunc as trunc(self) -> Self; - libm::fabs as abs(self) -> Self; - libm::fma as mul_add(self, a: Self, b: Self) -> Self; - libm::pow as powf(self, n: Self) -> Self; - libm::sqrt as sqrt(self) -> Self; - libm::exp as exp(self) -> Self; - libm::exp2 as exp2(self) -> Self; - libm::log as ln(self) -> Self; - libm::log2 as log2(self) -> Self; - libm::log10 as log10(self) -> Self; - libm::cbrt as cbrt(self) -> Self; - libm::hypot as hypot(self, other: Self) -> Self; - libm::sin as sin(self) -> Self; - libm::cos as cos(self) -> Self; - libm::tan as tan(self) -> Self; - libm::asin as asin(self) -> Self; - libm::acos as acos(self) -> Self; - libm::atan as atan(self) -> Self; - libm::atan2 as atan2(self, other: Self) -> Self; - libm::sincos as sin_cos(self) -> (Self, Self); - libm::expm1 as exp_m1(self) -> Self; - libm::log1p as ln_1p(self) -> Self; - libm::sinh as sinh(self) -> Self; - libm::cosh as cosh(self) -> Self; - libm::tanh as tanh(self) -> Self; - libm::asinh as asinh(self) -> Self; - libm::acosh as acosh(self) -> Self; - libm::atanh as atanh(self) -> Self; - libm::copysign as copysign(self, sign: Self) -> Self; - } -} - -macro_rules! float_const_impl { - ($(#[$doc:meta] $constant:ident,)+) => ( - #[allow(non_snake_case)] - pub trait FloatConst { - $(#[$doc] fn $constant() -> Self;)+ - #[doc = "Return the full circle constant `τ`."] - #[inline] - fn TAU() -> Self where Self: Sized + Add<Self, Output = Self> { - Self::PI() + Self::PI() - } - #[doc = "Return `log10(2.0)`."] - #[inline] - fn LOG10_2() -> Self where Self: Sized + Div<Self, Output = Self> { - Self::LN_2() / Self::LN_10() - } - #[doc = "Return `log2(10.0)`."] - #[inline] - fn LOG2_10() -> Self where Self: Sized + Div<Self, Output = Self> { - Self::LN_10() / Self::LN_2() - } - } - float_const_impl! { @float f32, $($constant,)+ } - float_const_impl! { @float f64, $($constant,)+ } - ); - (@float $T:ident, $($constant:ident,)+) => ( - impl FloatConst for $T { - constant! { - $( $constant() -> $T::consts::$constant; )+ - TAU() -> 6.28318530717958647692528676655900577; - LOG10_2() -> 0.301029995663981195213738894724493027; - LOG2_10() -> 3.32192809488736234787031942948939018; - } - } - ); -} - -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 `π`."] - PI, - #[doc = "Return `sqrt(2.0)`."] - SQRT_2, -} - -#[cfg(test)] -mod tests { - use core::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), - ]; - - #[test] - fn convert_deg_rad() { - use crate::float::FloatCore; - - for &(deg, rad) in &DEG_RAD_PAIRS { - assert!((FloatCore::to_degrees(rad) - deg).abs() < 1e-6); - assert!((FloatCore::to_radians(deg) - rad).abs() < 1e-6); - - let (deg, rad) = (deg as f32, rad as f32); - assert!((FloatCore::to_degrees(rad) - deg).abs() < 1e-5); - assert!((FloatCore::to_radians(deg) - rad).abs() < 1e-5); - } - } - - #[cfg(any(feature = "std", feature = "libm"))] - #[test] - fn convert_deg_rad_std() { - for &(deg, rad) in &DEG_RAD_PAIRS { - use crate::Float; - - 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-5); - assert!((Float::to_radians(deg) - rad).abs() < 1e-5); - } - } - - #[test] - fn to_degrees_rounding() { - use crate::float::FloatCore; - - assert_eq!( - FloatCore::to_degrees(1_f32), - 57.2957795130823208767981548141051703 - ); - } - - #[test] - #[cfg(any(feature = "std", feature = "libm"))] - fn extra_logs() { - use crate::float::{Float, FloatConst}; - - fn check<F: Float + FloatConst>(diff: F) { - let _2 = F::from(2.0).unwrap(); - assert!((F::LOG10_2() - F::log10(_2)).abs() < diff); - assert!((F::LOG10_2() - F::LN_2() / F::LN_10()).abs() < diff); - - let _10 = F::from(10.0).unwrap(); - assert!((F::LOG2_10() - F::log2(_10)).abs() < diff); - assert!((F::LOG2_10() - F::LN_10() / F::LN_2()).abs() < diff); - } - - check::<f32>(1e-6); - check::<f64>(1e-12); - } - - #[test] - #[cfg(any(feature = "std", feature = "libm"))] - fn copysign() { - use crate::float::Float; - test_copysign_generic(2.0_f32, -2.0_f32, f32::nan()); - test_copysign_generic(2.0_f64, -2.0_f64, f64::nan()); - test_copysignf(2.0_f32, -2.0_f32, f32::nan()); - } - - #[cfg(any(feature = "std", feature = "libm"))] - fn test_copysignf(p: f32, n: f32, nan: f32) { - use crate::float::Float; - use core::ops::Neg; - - assert!(p.is_sign_positive()); - assert!(n.is_sign_negative()); - assert!(nan.is_nan()); - - assert_eq!(p, Float::copysign(p, p)); - assert_eq!(p.neg(), Float::copysign(p, n)); - - assert_eq!(n, Float::copysign(n, n)); - assert_eq!(n.neg(), Float::copysign(n, p)); - - assert!(Float::copysign(nan, p).is_sign_positive()); - assert!(Float::copysign(nan, n).is_sign_negative()); - } - - #[cfg(any(feature = "std", feature = "libm"))] - fn test_copysign_generic<F: crate::float::Float + ::core::fmt::Debug>(p: F, n: F, nan: F) { - assert!(p.is_sign_positive()); - assert!(n.is_sign_negative()); - assert!(nan.is_nan()); - assert!(!nan.is_subnormal()); - - assert_eq!(p, p.copysign(p)); - assert_eq!(p.neg(), p.copysign(n)); - - assert_eq!(n, n.copysign(n)); - assert_eq!(n.neg(), n.copysign(p)); - - assert!(nan.copysign(p).is_sign_positive()); - assert!(nan.copysign(n).is_sign_negative()); - } - - #[cfg(any(feature = "std", feature = "libm"))] - fn test_subnormal<F: crate::float::Float + ::core::fmt::Debug>() { - let min_positive = F::min_positive_value(); - let lower_than_min = min_positive / F::from(2.0f32).unwrap(); - assert!(!min_positive.is_subnormal()); - assert!(lower_than_min.is_subnormal()); - } - - #[test] - #[cfg(any(feature = "std", feature = "libm"))] - fn subnormal() { - test_subnormal::<f64>(); - test_subnormal::<f32>(); - } -} |