2025 lines
52 KiB
Rust
2025 lines
52 KiB
Rust
use core::mem;
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use core::num::FpCategory;
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use core::ops::Neg;
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use core::f32;
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use core::f64;
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use {Num, NumCast, ToPrimitive};
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/// Generic trait for floating point numbers that works with `no_std`.
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///
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/// This trait implements a subset of the `Float` trait.
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pub trait FloatCore: Num + NumCast + Neg<Output = Self> + PartialOrd + Copy {
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/// Returns positive infinity.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T) {
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/// assert!(T::infinity() == x);
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/// }
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///
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/// check(f32::INFINITY);
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/// check(f64::INFINITY);
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/// ```
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fn infinity() -> Self;
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/// Returns negative infinity.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T) {
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/// assert!(T::neg_infinity() == x);
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/// }
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///
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/// check(f32::NEG_INFINITY);
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/// check(f64::NEG_INFINITY);
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/// ```
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fn neg_infinity() -> Self;
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/// Returns NaN.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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///
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/// fn check<T: FloatCore>() {
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/// let n = T::nan();
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/// assert!(n != n);
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/// }
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///
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/// check::<f32>();
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/// check::<f64>();
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/// ```
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fn nan() -> Self;
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/// Returns `-0.0`.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(n: T) {
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/// let z = T::neg_zero();
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/// assert!(z.is_zero());
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/// assert!(T::one() / z == n);
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/// }
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///
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/// check(f32::NEG_INFINITY);
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/// check(f64::NEG_INFINITY);
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/// ```
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fn neg_zero() -> Self;
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/// Returns the smallest finite value that this type can represent.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T) {
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/// assert!(T::min_value() == x);
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/// }
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///
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/// check(f32::MIN);
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/// check(f64::MIN);
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/// ```
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fn min_value() -> Self;
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/// Returns the smallest positive, normalized value that this type can represent.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T) {
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/// assert!(T::min_positive_value() == x);
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/// }
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///
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/// check(f32::MIN_POSITIVE);
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/// check(f64::MIN_POSITIVE);
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/// ```
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fn min_positive_value() -> Self;
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/// Returns epsilon, a small positive value.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T) {
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/// assert!(T::epsilon() == x);
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/// }
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///
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/// check(f32::EPSILON);
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/// check(f64::EPSILON);
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/// ```
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fn epsilon() -> Self;
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/// Returns the largest finite value that this type can represent.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T) {
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/// assert!(T::max_value() == x);
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/// }
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///
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/// check(f32::MAX);
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/// check(f64::MAX);
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/// ```
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fn max_value() -> Self;
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/// Returns `true` if the number is NaN.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T, p: bool) {
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/// assert!(x.is_nan() == p);
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/// }
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///
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/// check(f32::NAN, true);
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/// check(f32::INFINITY, false);
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/// check(f64::NAN, true);
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/// check(0.0f64, false);
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/// ```
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#[inline]
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fn is_nan(self) -> bool {
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self != self
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}
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/// Returns `true` if the number is infinite.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T, p: bool) {
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/// assert!(x.is_infinite() == p);
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/// }
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///
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/// check(f32::INFINITY, true);
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/// check(f32::NEG_INFINITY, true);
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/// check(f32::NAN, false);
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/// check(f64::INFINITY, true);
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/// check(f64::NEG_INFINITY, true);
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/// check(0.0f64, false);
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/// ```
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#[inline]
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fn is_infinite(self) -> bool {
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self == Self::infinity() || self == Self::neg_infinity()
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}
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/// Returns `true` if the number is neither infinite or NaN.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T, p: bool) {
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/// assert!(x.is_finite() == p);
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/// }
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///
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/// check(f32::INFINITY, false);
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/// check(f32::MAX, true);
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/// check(f64::NEG_INFINITY, false);
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/// check(f64::MIN_POSITIVE, true);
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/// check(f64::NAN, false);
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/// ```
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#[inline]
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fn is_finite(self) -> bool {
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!(self.is_nan() || self.is_infinite())
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}
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/// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T, p: bool) {
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/// assert!(x.is_normal() == p);
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/// }
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///
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/// check(f32::INFINITY, false);
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/// check(f32::MAX, true);
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/// check(f64::NEG_INFINITY, false);
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/// check(f64::MIN_POSITIVE, true);
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/// check(0.0f64, false);
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/// ```
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#[inline]
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fn is_normal(self) -> bool {
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self.classify() == FpCategory::Normal
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}
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/// Returns the floating point category of the number. If only one property
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/// is going to be tested, it is generally faster to use the specific
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/// predicate instead.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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/// use std::num::FpCategory;
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///
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/// fn check<T: FloatCore>(x: T, c: FpCategory) {
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/// assert!(x.classify() == c);
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/// }
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///
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/// check(f32::INFINITY, FpCategory::Infinite);
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/// check(f32::MAX, FpCategory::Normal);
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/// check(f64::NAN, FpCategory::Nan);
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/// check(f64::MIN_POSITIVE, FpCategory::Normal);
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/// check(f64::MIN_POSITIVE / 2.0, FpCategory::Subnormal);
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/// check(0.0f64, FpCategory::Zero);
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/// ```
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fn classify(self) -> FpCategory;
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/// Returns the largest integer less than or equal to a number.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T, y: T) {
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/// assert!(x.floor() == y);
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/// }
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///
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/// check(f32::INFINITY, f32::INFINITY);
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/// check(0.9f32, 0.0);
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/// check(1.0f32, 1.0);
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/// check(1.1f32, 1.0);
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/// check(-0.0f64, 0.0);
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/// check(-0.9f64, -1.0);
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/// check(-1.0f64, -1.0);
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/// check(-1.1f64, -2.0);
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/// check(f64::MIN, f64::MIN);
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/// ```
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#[inline]
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fn floor(self) -> Self {
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let f = self.fract();
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if f.is_nan() || f.is_zero() {
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self
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} else if self < Self::zero() {
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self - f - Self::one()
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} else {
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self - f
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}
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}
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/// Returns the smallest integer greater than or equal to a number.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T, y: T) {
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/// assert!(x.ceil() == y);
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/// }
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///
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/// check(f32::INFINITY, f32::INFINITY);
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/// check(0.9f32, 1.0);
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/// check(1.0f32, 1.0);
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/// check(1.1f32, 2.0);
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/// check(-0.0f64, 0.0);
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/// check(-0.9f64, -0.0);
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/// check(-1.0f64, -1.0);
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/// check(-1.1f64, -1.0);
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/// check(f64::MIN, f64::MIN);
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/// ```
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#[inline]
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fn ceil(self) -> Self {
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let f = self.fract();
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if f.is_nan() || f.is_zero() {
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self
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} else if self > Self::zero() {
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self - f + Self::one()
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} else {
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self - f
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}
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}
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/// Returns the nearest integer to a number. Round half-way cases away from `0.0`.
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///
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/// # Examples
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T, y: T) {
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/// assert!(x.round() == y);
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/// }
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///
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/// check(f32::INFINITY, f32::INFINITY);
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/// check(0.4f32, 0.0);
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/// check(0.5f32, 1.0);
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/// check(0.6f32, 1.0);
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/// check(-0.4f64, 0.0);
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/// check(-0.5f64, -1.0);
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/// check(-0.6f64, -1.0);
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/// check(f64::MIN, f64::MIN);
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/// ```
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#[inline]
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fn round(self) -> Self {
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let one = Self::one();
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let h = Self::from(0.5).expect("Unable to cast from 0.5");
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let f = self.fract();
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if f.is_nan() || f.is_zero() {
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self
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} else if self > Self::zero() {
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if f < h {
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self - f
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} else {
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self - f + one
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}
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} else {
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if -f < h {
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self - f
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} else {
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self - f - one
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}
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}
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}
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/// Return the integer part of a number.
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///
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/// # Examples
|
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///
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/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T, y: T) {
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/// assert!(x.trunc() == y);
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/// }
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///
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/// check(f32::INFINITY, f32::INFINITY);
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/// check(0.9f32, 0.0);
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/// check(1.0f32, 1.0);
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/// check(1.1f32, 1.0);
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/// check(-0.0f64, 0.0);
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/// check(-0.9f64, -0.0);
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/// check(-1.0f64, -1.0);
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/// check(-1.1f64, -1.0);
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/// check(f64::MIN, f64::MIN);
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/// ```
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#[inline]
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fn trunc(self) -> Self {
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let f = self.fract();
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if f.is_nan() {
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self
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} else {
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self - f
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}
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}
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/// Returns the fractional part of a number.
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///
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/// # Examples
|
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///
|
||
/// ```
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/// use num_traits::float::FloatCore;
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/// use std::{f32, f64};
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///
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/// fn check<T: FloatCore>(x: T, y: T) {
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/// assert!(x.fract() == y);
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/// }
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///
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/// check(f32::MAX, 0.0);
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/// check(0.75f32, 0.75);
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/// check(1.0f32, 0.0);
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/// check(1.25f32, 0.25);
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/// check(-0.0f64, 0.0);
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/// check(-0.75f64, -0.75);
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/// check(-1.0f64, 0.0);
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/// check(-1.25f64, -0.25);
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/// check(f64::MIN, 0.0);
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/// ```
|
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#[inline]
|
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fn fract(self) -> Self {
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if self.is_zero() {
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Self::zero()
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} else {
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self % Self::one()
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}
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}
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|
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/// Computes the absolute value of `self`. Returns `FloatCore::nan()` if the
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/// number is `FloatCore::nan()`.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// use num_traits::float::FloatCore;
|
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/// use std::{f32, f64};
|
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///
|
||
/// fn check<T: FloatCore>(x: T, y: T) {
|
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/// assert!(x.abs() == y);
|
||
/// }
|
||
///
|
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/// check(f32::INFINITY, f32::INFINITY);
|
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/// check(1.0f32, 1.0);
|
||
/// check(0.0f64, 0.0);
|
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/// 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 since Rust 1.20 also
|
||
/// `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, 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 since Rust 1.20 also
|
||
/// `-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);
|
||
/// ```
|
||
#[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, min: T) {
|
||
/// assert!(x.max(y) == min);
|
||
/// }
|
||
///
|
||
/// 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)
|
||
}
|
||
|
||
#[inline]
|
||
#[cfg(not(feature = "std"))]
|
||
fn classify(self) -> FpCategory {
|
||
const EXP_MASK: u32 = 0x7f800000;
|
||
const MAN_MASK: u32 = 0x007fffff;
|
||
|
||
let bits: u32 = unsafe { mem::transmute(self) };
|
||
match (bits & MAN_MASK, bits & EXP_MASK) {
|
||
(0, 0) => FpCategory::Zero,
|
||
(_, 0) => FpCategory::Subnormal,
|
||
(0, EXP_MASK) => FpCategory::Infinite,
|
||
(_, EXP_MASK) => FpCategory::Nan,
|
||
_ => FpCategory::Normal,
|
||
}
|
||
}
|
||
|
||
#[inline]
|
||
#[cfg(not(feature = "std"))]
|
||
fn to_degrees(self) -> Self {
|
||
// Use a constant for better precision.
|
||
const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
|
||
self * PIS_IN_180
|
||
}
|
||
|
||
#[inline]
|
||
#[cfg(not(feature = "std"))]
|
||
fn to_radians(self) -> Self {
|
||
self * (f32::consts::PI / 180.0)
|
||
}
|
||
|
||
#[cfg(feature = "std")]
|
||
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::min(self, other: Self) -> Self;
|
||
Self::max(self, other: Self) -> Self;
|
||
Self::recip(self) -> Self;
|
||
Self::powi(self, n: i32) -> Self;
|
||
Self::to_degrees(self) -> Self;
|
||
Self::to_radians(self) -> 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)
|
||
}
|
||
|
||
#[inline]
|
||
#[cfg(not(feature = "std"))]
|
||
fn classify(self) -> FpCategory {
|
||
const EXP_MASK: u64 = 0x7ff0000000000000;
|
||
const MAN_MASK: u64 = 0x000fffffffffffff;
|
||
|
||
let bits: u64 = unsafe { mem::transmute(self) };
|
||
match (bits & MAN_MASK, bits & EXP_MASK) {
|
||
(0, 0) => FpCategory::Zero,
|
||
(_, 0) => FpCategory::Subnormal,
|
||
(0, EXP_MASK) => FpCategory::Infinite,
|
||
(_, EXP_MASK) => FpCategory::Nan,
|
||
_ => FpCategory::Normal,
|
||
}
|
||
}
|
||
|
||
#[inline]
|
||
#[cfg(not(feature = "std"))]
|
||
fn to_degrees(self) -> Self {
|
||
// The division here is correctly rounded with respect to the true
|
||
// value of 180/π. (This differs from f32, where a constant must be
|
||
// used to ensure a correctly rounded result.)
|
||
self * (180.0 / f64::consts::PI)
|
||
}
|
||
|
||
#[inline]
|
||
#[cfg(not(feature = "std"))]
|
||
fn to_radians(self) -> Self {
|
||
self * (f64::consts::PI / 180.0)
|
||
}
|
||
|
||
#[cfg(feature = "std")]
|
||
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::min(self, other: Self) -> Self;
|
||
Self::max(self, other: Self) -> Self;
|
||
Self::recip(self) -> Self;
|
||
Self::powi(self, n: i32) -> Self;
|
||
Self::to_degrees(self) -> Self;
|
||
Self::to_radians(self) -> 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.
|
||
#[cfg(feature = "std")]
|
||
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 since Rust 1.20 also `Float::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 since Rust 1.20 also `-Float::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, 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);
|
||
}
|
||
|
||
#[cfg(feature = "std")]
|
||
macro_rules! float_impl {
|
||
($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;
|
||
}
|
||
}
|
||
};
|
||
}
|
||
|
||
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)
|
||
}
|
||
|
||
#[cfg(feature = "std")]
|
||
float_impl!(f32 integer_decode_f32);
|
||
#[cfg(feature = "std")]
|
||
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 {
|
||
constant! {
|
||
$( $constant() -> $T::consts::$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 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 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(feature = "std")]
|
||
#[test]
|
||
fn convert_deg_rad_std() {
|
||
for &(deg, rad) in &DEG_RAD_PAIRS {
|
||
use 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]
|
||
// This fails with the forwarded `std` implementation in Rust 1.8.
|
||
// To avoid the failure, the test is limited to `no_std` builds.
|
||
#[cfg(not(feature = "std"))]
|
||
fn to_degrees_rounding() {
|
||
use float::FloatCore;
|
||
|
||
assert_eq!(
|
||
FloatCore::to_degrees(1_f32),
|
||
57.2957795130823208767981548141051703
|
||
);
|
||
}
|
||
}
|