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-rw-r--r--third_party/rust/num-traits/src/float.rs2351
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diff --git a/third_party/rust/num-traits/src/float.rs b/third_party/rust/num-traits/src/float.rs
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+++ b/third_party/rust/num-traits/src/float.rs
@@ -0,0 +1,2351 @@
+use core::mem;
+use core::num::FpCategory;
+use core::ops::{Add, Div, Neg};
+
+use core::f32;
+use core::f64;
+
+use {Num, NumCast, ToPrimitive};
+
+#[cfg(all(not(feature = "std"), feature = "libm"))]
+use libm;
+
+/// 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]
+ 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 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 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, 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)
+ }
+
+ #[inline]
+ #[cfg(not(feature = "std"))]
+ fn classify(self) -> FpCategory {
+ const EXP_MASK: u32 = 0x7f800000;
+ const MAN_MASK: u32 = 0x007fffff;
+
+ // Safety: this identical to the implementation of f32::to_bits(),
+ // which is only available starting at Rust 1.20
+ 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 is_sign_negative(self) -> bool {
+ const SIGN_MASK: u32 = 0x80000000;
+
+ // Safety: this identical to the implementation of f32::to_bits(),
+ // which is only available starting at Rust 1.20
+ let bits: u32 = unsafe { mem::transmute(self) };
+ bits & SIGN_MASK != 0
+ }
+
+ #[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;
+ }
+
+ #[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;
+ libm::fminf as min(self, other: Self) -> Self;
+ libm::fmaxf as max(self, other: 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)
+ }
+
+ #[inline]
+ #[cfg(not(feature = "std"))]
+ fn classify(self) -> FpCategory {
+ const EXP_MASK: u64 = 0x7ff0000000000000;
+ const MAN_MASK: u64 = 0x000fffffffffffff;
+
+ // Safety: this identical to the implementation of f64::to_bits(),
+ // which is only available starting at Rust 1.20
+ 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 is_sign_negative(self) -> bool {
+ const SIGN_MASK: u64 = 0x8000000000000000;
+
+ // Safety: this identical to the implementation of f64::to_bits(),
+ // which is only available starting at Rust 1.20
+ let bits: u64 = unsafe { mem::transmute(self) };
+ bits & SIGN_MASK != 0
+ }
+
+ #[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;
+ }
+
+ #[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;
+ libm::fmin as min(self, other: Self) -> Self;
+ libm::fmax as max(self, other: 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/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);
+
+ /// 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) {
+ $decode(self)
+ }
+
+ forward! {
+ Self::is_nan(self) -> bool;
+ Self::is_infinite(self) -> bool;
+ Self::is_finite(self) -> bool;
+ Self::is_normal(self) -> bool;
+ Self::classify(self) -> FpCategory;
+ Self::floor(self) -> Self;
+ Self::ceil(self) -> Self;
+ Self::round(self) -> Self;
+ Self::trunc(self) -> Self;
+ Self::fract(self) -> Self;
+ Self::abs(self) -> Self;
+ Self::signum(self) -> Self;
+ Self::is_sign_positive(self) -> bool;
+ Self::is_sign_negative(self) -> bool;
+ Self::mul_add(self, a: Self, b: Self) -> Self;
+ Self::recip(self) -> Self;
+ Self::powi(self, n: i32) -> Self;
+ Self::powf(self, n: Self) -> Self;
+ Self::sqrt(self) -> Self;
+ Self::exp(self) -> Self;
+ Self::exp2(self) -> Self;
+ Self::ln(self) -> Self;
+ Self::log(self, base: Self) -> Self;
+ Self::log2(self) -> Self;
+ Self::log10(self) -> Self;
+ Self::to_degrees(self) -> Self;
+ Self::to_radians(self) -> Self;
+ Self::max(self, other: Self) -> Self;
+ Self::min(self, other: Self) -> Self;
+ Self::cbrt(self) -> Self;
+ Self::hypot(self, other: Self) -> Self;
+ Self::sin(self) -> Self;
+ Self::cos(self) -> Self;
+ Self::tan(self) -> Self;
+ Self::asin(self) -> Self;
+ Self::acos(self) -> Self;
+ Self::atan(self) -> Self;
+ Self::atan2(self, other: Self) -> Self;
+ Self::sin_cos(self) -> (Self, Self);
+ Self::exp_m1(self) -> Self;
+ Self::ln_1p(self) -> Self;
+ Self::sinh(self) -> Self;
+ Self::cosh(self) -> Self;
+ Self::tanh(self) -> Self;
+ Self::asinh(self) -> Self;
+ Self::acosh(self) -> Self;
+ Self::atanh(self) -> Self;
+ }
+
+ #[cfg(has_copysign)]
+ #[inline]
+ fn copysign(self, sign: Self) -> Self {
+ Self::copysign(self, sign)
+ }
+ }
+ };
+}
+
+#[cfg(all(not(feature = "std"), feature = "libm"))]
+macro_rules! float_impl_libm {
+ ($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! {
+ FloatCore::is_nan(self) -> bool;
+ FloatCore::is_infinite(self) -> bool;
+ FloatCore::is_finite(self) -> bool;
+ FloatCore::is_normal(self) -> bool;
+ FloatCore::classify(self) -> FpCategory;
+ FloatCore::signum(self) -> Self;
+ FloatCore::is_sign_positive(self) -> bool;
+ FloatCore::is_sign_negative(self) -> bool;
+ FloatCore::recip(self) -> Self;
+ FloatCore::powi(self, n: i32) -> Self;
+ FloatCore::to_degrees(self) -> Self;
+ FloatCore::to_radians(self) -> Self;
+ }
+ };
+}
+
+fn integer_decode_f32(f: f32) -> (u64, i16, i8) {
+ // Safety: this identical to the implementation of f32::to_bits(),
+ // which is only available starting at Rust 1.20
+ 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) {
+ // Safety: this identical to the implementation of f64::to_bits(),
+ // which is only available starting at Rust 1.20
+ 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_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::fmaxf as max(self, other: Self) -> Self;
+ libm::fminf as min(self, other: 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::fmax as max(self, other: Self) -> Self;
+ libm::fmin as min(self, other: 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 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 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
+ );
+ }
+
+ #[test]
+ #[cfg(any(feature = "std", feature = "libm"))]
+ fn extra_logs() {
+ use 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 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 core::ops::Neg;
+ use float::Float;
+
+ 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));
+
+ // FIXME: is_sign... only works on NaN starting in Rust 1.20
+ // 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: ::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_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));
+
+ // FIXME: is_sign... only works on NaN starting in Rust 1.20
+ // assert!(nan.copysign(p).is_sign_positive());
+ // assert!(nan.copysign(n).is_sign_negative());
+ }
+}
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