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//! Extension trait for full float functionality in `#[no_std]` backed by [`libm`].
//!
//! Method signatures, implementation, and documentation are copied from as `std` 1.72,
//! with calls to instrinsics replaced by their `libm` equivalents.
//!
//! # Usage
//! ```rust
//! #[allow(unused_imports)] // will be unused on std targets
//! use core_maths::*;
//!
//! 3.9.floor();
//! ```
#![no_std]
#![warn(missing_docs)]
/// See [`crate`].
pub trait CoreFloat: Sized + Copy {
/// Returns the largest integer less than or equal to `self`.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let f = 3.7_f64;
/// let g = 3.0_f64;
/// let h = -3.7_f64;
///
/// assert_eq!(CoreFloat::floor(f), 3.0);
/// assert_eq!(CoreFloat::floor(g), 3.0);
/// assert_eq!(CoreFloat::floor(h), -4.0);
/// ```
fn floor(self) -> Self;
/// Returns the smallest integer greater than or equal to `self`.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let f = 3.01_f64;
/// let g = 4.0_f64;
///
/// assert_eq!(CoreFloat::ceil(f), 4.0);
/// assert_eq!(CoreFloat::ceil(g), 4.0);
/// ```
fn ceil(self) -> Self;
/// Returns the nearest integer to `self`. If a value is half-way between two
/// integers, round away from `0.0`.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let f = 3.3_f64;
/// let g = -3.3_f64;
/// let h = -3.7_f64;
/// let i = 3.5_f64;
/// let j = 4.5_f64;
///
/// assert_eq!(CoreFloat::round(f), 3.0);
/// assert_eq!(CoreFloat::round(g), -3.0);
/// assert_eq!(CoreFloat::round(h), -4.0);
/// assert_eq!(CoreFloat::round(i), 4.0);
/// assert_eq!(CoreFloat::round(j), 5.0);
/// ```
fn round(self) -> Self;
/// Returns the integer part of `self`.
/// This means that non-integer numbers are always truncated towards zero.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let f = 3.7_f64;
/// let g = 3.0_f64;
/// let h = -3.7_f64;
///
/// assert_eq!(CoreFloat::trunc(f), 3.0);
/// assert_eq!(CoreFloat::trunc(g), 3.0);
/// assert_eq!(CoreFloat::trunc(h), -3.0);
/// ```
fn trunc(self) -> Self;
/// Returns the fractional part of `self`.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 3.6_f64;
/// let y = -3.6_f64;
/// let abs_difference_x = (CoreFloat::fract(x) - CoreFloat::abs(0.6));
/// let abs_difference_y = (CoreFloat::fract(y) - CoreFloat::abs(-0.6));
///
/// assert!(abs_difference_x < 1e-10);
/// assert!(abs_difference_y < 1e-10);
/// ```
fn fract(self) -> Self;
/// Computes the absolute value of `self`.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 3.5_f64;
/// let y = -3.5_f64;
///
/// let abs_difference_x = (CoreFloat::abs(x) - CoreFloat::abs(x));
/// let abs_difference_y = (CoreFloat::abs(y) - (CoreFloat::abs(-y)));
///
/// 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 `INFINITY`
/// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
/// - NaN if the number is NaN
///
/// This method does not use an intrinsic in `std`, so its code is copied.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let f = 3.5_f64;
///
/// assert_eq!(CoreFloat::signum(f), 1.0);
/// assert_eq!(CoreFloat::signum(f64::NEG_INFINITY), -1.0);
///
/// assert!(CoreFloat::signum(f64::NAN).is_nan());
/// ```
fn signum(self) -> Self;
/// 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 bit of
/// `sign` is returned. Note, however, that conserving the sign bit on NaN
/// across arithmetical operations is not generally guaranteed.
/// See [explanation of NaN as a special value](primitive@f32) for more info.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let f = 3.5_f64;
///
/// assert_eq!(CoreFloat::copysign(f, 0.42), 3.5_f64);
/// assert_eq!(CoreFloat::copysign(f, -0.42), -3.5_f64);
/// assert_eq!(CoreFloat::copysign(-f, 0.42), 3.5_f64);
/// assert_eq!(CoreFloat::copysign(-f, -0.42), -3.5_f64);
///
/// assert!(CoreFloat::copysign(f64::NAN, 1.0).is_nan());
/// ```
fn copysign(self, sign: Self) -> Self;
/// 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` *may* be more performant than an unfused multiply-add if
/// the target architecture has a dedicated `fma` CPU instruction. However,
/// this is not always true, and will be heavily dependant on designing
/// algorithms with specific target hardware in mind.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let m = 10.0_f64;
/// let x = 4.0_f64;
/// let b = 60.0_f64;
///
/// // 100.0
/// let abs_difference = (CoreFloat::mul_add(m, x, b) - ((m * x) + b)).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn mul_add(self, a: Self, b: Self) -> Self;
/// Calculates Euclidean division, the matching method for `rem_euclid`.
///
/// This computes the integer `n` such that
/// `self = n * rhs + self.rem_euclid(rhs)`.
/// In other words, the result is `self / rhs` rounded to the integer `n`
/// such that `self >= n * rhs`.
///
/// This method does not use an intrinsic in `std`, so its code is copied.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let a: f64 = 7.0;
/// let b = 4.0;
/// assert_eq!(CoreFloat::div_euclid(a, b), 1.0); // 7.0 > 4.0 * 1.0
/// assert_eq!(CoreFloat::div_euclid(-a, b), -2.0); // -7.0 >= 4.0 * -2.0
/// assert_eq!(CoreFloat::div_euclid(a, -b), -1.0); // 7.0 >= -4.0 * -1.0
/// assert_eq!(CoreFloat::div_euclid(-a, -b), 2.0); // -7.0 >= -4.0 * 2.0
/// ```
fn div_euclid(self, rhs: Self) -> Self;
/// Calculates the least nonnegative remainder of `self (mod rhs)`.
///
/// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
/// most cases. However, due to a floating point round-off error it can
/// result in `r == rhs.abs()`, violating the mathematical definition, if
/// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
/// This result is not an element of the function's codomain, but it is the
/// closest floating point number in the real numbers and thus fulfills the
/// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
/// approximately.
///
/// This method does not use an intrinsic in `std`, so its code is copied.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let a: f64 = 7.0;
/// let b = 4.0;
/// assert_eq!(CoreFloat::rem_euclid(a, b), 3.0);
/// assert_eq!(CoreFloat::rem_euclid(-a, b), 1.0);
/// assert_eq!(CoreFloat::rem_euclid(a, -b), 3.0);
/// assert_eq!(CoreFloat::rem_euclid(-a, -b), 1.0);
/// // limitation due to round-off error
/// assert!(CoreFloat::rem_euclid(-f64::EPSILON, 3.0) != 0.0);
/// ```
fn rem_euclid(self, rhs: Self) -> Self;
/// Raises a number to an integer power.
///
/// Using this function is generally faster than using `powf`.
/// It might have a different sequence of rounding operations than `powf`,
/// so the results are not guaranteed to agree.
///
/// This method is not available in `libm`, so it uses a custom implementation.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 2.0_f64;
/// let abs_difference = (CoreFloat::powi(x, 2) - (x * x)).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn powi(self, n: i32) -> Self;
/// Raises a number to a floating point power.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 2.0_f64;
/// let abs_difference = (CoreFloat::powf(x, 2.0) - (x * x)).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn powf(self, n: Self) -> Self;
/// Returns the square root of a number.
///
/// Returns NaN if `self` is a negative number other than `-0.0`.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let positive = 4.0_f64;
/// let negative = -4.0_f64;
/// let negative_zero = -0.0_f64;
///
/// let abs_difference = (CoreFloat::sqrt(positive) - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// assert!(CoreFloat::sqrt(negative).is_nan());
/// assert!(CoreFloat::sqrt(negative_zero) == negative_zero);
/// ```
fn sqrt(self) -> Self;
/// Returns `e^(self)`, (the exponential function).
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let one = 1.0_f64;
/// // e^1
/// let e = CoreFloat::exp(one);
///
/// // ln(e) - 1 == 0
/// let abs_difference = (e.ln() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn exp(self) -> Self;
/// Returns `2^(self)`.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let f = 2.0_f64;
///
/// // 2^2 - 4 == 0
/// let abs_difference = (CoreFloat::exp2(f) - 4.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn exp2(self) -> Self;
/// Returns the natural logarithm of the number.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let one = 1.0_f64;
/// // e^1
/// let e = one.exp();
///
/// // ln(e) - 1 == 0
/// let abs_difference = (CoreFloat::ln(e) - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn ln(self) -> Self;
/// Returns the logarithm of the number with respect to an arbitrary base.
///
/// The result might not be correctly rounded owing to implementation details;
/// `self.log2()` can produce more accurate results for base 2, and
/// `self.log10()` can produce more accurate results for base 10.
///
/// This method does not use an intrinsic in `std`, so its code is copied.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let twenty_five = 25.0_f64;
///
/// // log5(25) - 2 == 0
/// let abs_difference = (CoreFloat::log(twenty_five, 5.0) - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn log(self, base: Self) -> Self;
/// Returns the base 2 logarithm of the number.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let four = 4.0_f64;
///
/// // log2(4) - 2 == 0
/// let abs_difference = (CoreFloat::log2(four) - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn log2(self) -> Self;
/// Returns the base 10 logarithm of the number.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let hundred = 100.0_f64;
///
/// // log10(100) - 2 == 0
/// let abs_difference = (CoreFloat::log10(hundred) - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn log10(self) -> Self;
/// Returns the cube root of a number.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 8.0_f64;
///
/// // x^(1/3) - 2 == 0
/// let abs_difference = (CoreFloat::cbrt(x) - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn cbrt(self) -> Self;
/// Compute the distance between the origin and a point (`x`, `y`) on the
/// Euclidean plane. Equivalently, compute the length of the hypotenuse of a
/// right-angle triangle with other sides having length `x.abs()` and
/// `y.abs()`.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 2.0_f64;
/// let y = 3.0_f64;
///
/// // sqrt(x^2 + y^2)
/// let abs_difference = (CoreFloat::hypot(x, 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).
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = std::f64::consts::FRAC_PI_2;
///
/// let abs_difference = (CoreFloat::sin(x) - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn sin(self) -> Self;
/// Computes the cosine of a number (in radians).
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 2.0 * std::f64::consts::PI;
///
/// let abs_difference = (CoreFloat::cos(x) - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn cos(self) -> Self;
/// Computes the tangent of a number (in radians).
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = std::f64::consts::FRAC_PI_4;
///
/// let abs_difference = (CoreFloat::tan(x) - 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].
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let f = std::f64::consts::FRAC_PI_2;
///
/// // asin(sin(pi/2))
/// let abs_difference = (CoreFloat::asin(f.sin()) - std::f64::consts::FRAC_PI_2).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].
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let f = std::f64::consts::FRAC_PI_4;
///
/// // acos(cos(pi/4))
/// let abs_difference = (CoreFloat::acos(f.cos()) - std::f64::consts::FRAC_PI_4).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];
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let f = 1.0_f64;
///
/// // atan(tan(1))
/// let abs_difference = (CoreFloat::atan(f.tan()) - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
fn atan(self) -> Self;
/// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
///
/// * `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)`
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// // Positive angles measured counter-clockwise
/// // from positive x axis
/// // -pi/4 radians (45 deg clockwise)
/// let x1 = 3.0_f64;
/// let y1 = -3.0_f64;
///
/// // 3pi/4 radians (135 deg counter-clockwise)
/// let x2 = -3.0_f64;
/// let y2 = 3.0_f64;
///
/// let abs_difference_1 = (CoreFloat::atan2(y1, x1) - (-std::f64::consts::FRAC_PI_4)).abs();
/// let abs_difference_2 = (CoreFloat::atan2(y2, x2) - (3.0 * std::f64::consts::FRAC_PI_4)).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))`.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = std::f64::consts::FRAC_PI_4;
/// let f = CoreFloat::sin_cos(x);
///
/// 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_1 < 1e-10);
/// ```
fn sin_cos(self) -> (Self, Self) {
(self.sin(), self.cos())
}
/// Returns `e^(self) - 1` in a way that is accurate even if the
/// number is close to zero.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 1e-16_f64;
///
/// // for very small x, e^x is approximately 1 + x + x^2 / 2
/// let approx = x + x * x / 2.0;
/// let abs_difference = (CoreFloat::exp_m1(x) - approx).abs();
///
/// assert!(abs_difference < 1e-20);
/// ```
fn exp_m1(self) -> Self;
/// Returns `ln(1+n)` (natural logarithm) more accurately than if
/// the operations were performed separately.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 1e-16_f64;
///
/// // for very small x, ln(1 + x) is approximately x - x^2 / 2
/// let approx = x - x * x / 2.0;
/// let abs_difference = (CoreFloat::ln_1p(x) - approx).abs();
///
/// assert!(abs_difference < 1e-20);
/// ```
fn ln_1p(self) -> Self;
/// Hyperbolic sine function.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let e = std::f64::consts::E;
/// let x = 1.0_f64;
///
/// let f = CoreFloat::sinh(x);
/// // 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.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let e = std::f64::consts::E;
/// let x = 1.0_f64;
/// let f = CoreFloat::cosh(x);
/// // 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.
///
/// This implementation uses `libm` instead of the Rust intrinsic.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let e = std::f64::consts::E;
/// let x = 1.0_f64;
///
/// let f = CoreFloat::tanh(x);
/// // 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.
///
/// This method does not use an intrinsic in `std`, so its code is copied.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 1.0_f64;
/// let f = CoreFloat::asinh(x.sinh());
///
/// let abs_difference = (f - x).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn asinh(self) -> Self;
/// Inverse hyperbolic cosine function.
///
/// This method does not use an intrinsic in `std`, so its code is copied.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let x = 1.0_f64;
/// let f = CoreFloat::acosh(x.cosh());
///
/// let abs_difference = (f - x).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn acosh(self) -> Self;
/// Inverse hyperbolic tangent function.
///
/// This method does not use an intrinsic in `std`, so its code is copied.
///
/// # Examples
///
/// ```
/// use core_maths::*;
/// let e = std::f64::consts::E;
/// let f = CoreFloat::atanh(e.tanh());
///
/// let abs_difference = (f - e).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
fn atanh(self) -> Self;
}
impl CoreFloat for f32 {
#[inline]
fn floor(self) -> Self {
libm::floorf(self)
}
#[inline]
fn ceil(self) -> Self {
libm::ceilf(self)
}
#[inline]
fn round(self) -> Self {
libm::roundf(self)
}
#[inline]
fn trunc(self) -> Self {
libm::truncf(self)
}
#[inline]
fn fract(self) -> Self {
self - self.trunc()
}
#[inline]
fn abs(self) -> Self {
libm::fabsf(self)
}
#[inline]
fn signum(self) -> Self {
if self.is_nan() {
Self::NAN
} else {
1.0_f32.copysign(self)
}
}
#[inline]
fn copysign(self, sign: Self) -> Self {
libm::copysignf(self, sign)
}
#[inline]
fn mul_add(self, a: Self, b: Self) -> Self {
libm::fmaf(self, a, b)
}
#[inline]
fn div_euclid(self, rhs: Self) -> Self {
let q = (self / rhs).trunc();
if self % rhs < 0.0 {
return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
}
q
}
#[inline]
fn rem_euclid(self, rhs: Self) -> Self {
let r = self % rhs;
if r < 0.0 {
r + rhs.abs()
} else {
r
}
}
#[inline]
fn powi(self, exp: i32) -> Self {
if exp == 0 {
return 1.0;
}
let mut base = if exp < 0 { self.recip() } else { self };
let mut exp = exp.unsigned_abs();
let mut acc = 1.0;
while exp > 1 {
if (exp & 1) == 1 {
acc *= base;
}
exp /= 2;
base = base * base;
}
// since exp!=0, finally the exp must be 1.
// Deal with the final bit of the exponent separately, since
// squaring the base afterwards is not necessary and may cause a
// needless overflow.
acc * base
}
#[inline]
fn powf(self, n: Self) -> Self {
libm::powf(self, n)
}
#[inline]
fn sqrt(self) -> Self {
libm::sqrtf(self)
}
#[inline]
fn exp(self) -> Self {
libm::expf(self)
}
#[inline]
fn exp2(self) -> Self {
libm::exp2f(self)
}
#[inline]
fn ln(self) -> Self {
libm::logf(self)
}
#[inline]
fn log(self, base: Self) -> Self {
self.ln() / base.ln()
}
#[inline]
fn log2(self) -> Self {
libm::log2f(self)
}
#[inline]
fn log10(self) -> Self {
libm::log10f(self)
}
#[inline]
fn cbrt(self) -> Self {
libm::cbrtf(self)
}
#[inline]
fn hypot(self, other: Self) -> Self {
libm::hypotf(self, other)
}
#[inline]
fn sin(self) -> Self {
libm::sinf(self)
}
#[inline]
fn cos(self) -> Self {
libm::cosf(self)
}
#[inline]
fn tan(self) -> Self {
libm::tanf(self)
}
#[inline]
fn asin(self) -> Self {
libm::asinf(self)
}
#[inline]
fn acos(self) -> Self {
libm::acosf(self)
}
#[inline]
fn atan(self) -> Self {
libm::atanf(self)
}
#[inline]
fn atan2(self, other: Self) -> Self {
libm::atan2f(self, other)
}
#[inline]
fn exp_m1(self) -> Self {
libm::expm1f(self)
}
#[inline]
fn ln_1p(self) -> Self {
libm::log1pf(self)
}
#[inline]
fn sinh(self) -> Self {
libm::sinhf(self)
}
#[inline]
fn cosh(self) -> Self {
libm::coshf(self)
}
#[inline]
fn tanh(self) -> Self {
libm::tanhf(self)
}
#[inline]
fn asinh(self) -> Self {
let ax = self.abs();
let ix = 1.0 / ax;
(ax + (ax / (Self::hypot(1.0, ix) + ix)))
.ln_1p()
.copysign(self)
}
#[inline]
fn acosh(self) -> Self {
if self < 1.0 {
Self::NAN
} else {
(self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
}
}
#[inline]
fn atanh(self) -> Self {
0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
}
}
impl CoreFloat for f64 {
#[inline]
fn floor(self) -> Self {
libm::floor(self)
}
#[inline]
fn ceil(self) -> Self {
libm::ceil(self)
}
#[inline]
fn round(self) -> Self {
libm::round(self)
}
#[inline]
fn trunc(self) -> Self {
libm::trunc(self)
}
#[inline]
fn fract(self) -> Self {
self - self.trunc()
}
#[inline]
fn abs(self) -> Self {
libm::fabs(self)
}
#[inline]
fn signum(self) -> Self {
if self.is_nan() {
Self::NAN
} else {
1.0_f64.copysign(self)
}
}
#[inline]
fn copysign(self, sign: Self) -> Self {
libm::copysign(self, sign)
}
#[inline]
fn mul_add(self, a: Self, b: Self) -> Self {
libm::fma(self, a, b)
}
#[inline]
fn div_euclid(self, rhs: Self) -> Self {
let q = (self / rhs).trunc();
if self % rhs < 0.0 {
return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
}
q
}
#[inline]
fn rem_euclid(self, rhs: Self) -> Self {
let r = self % rhs;
if r < 0.0 {
r + rhs.abs()
} else {
r
}
}
#[inline]
fn powi(self, exp: i32) -> Self {
if exp == 0 {
return 1.0;
}
let mut base = if exp < 0 { self.recip() } else { self };
let mut exp = exp.unsigned_abs();
let mut acc = 1.0;
while exp > 1 {
if (exp & 1) == 1 {
acc *= base;
}
exp /= 2;
base = base * base;
}
// since exp!=0, finally the exp must be 1.
// Deal with the final bit of the exponent separately, since
// squaring the base afterwards is not necessary and may cause a
// needless overflow.
acc * base
}
#[inline]
fn powf(self, n: Self) -> Self {
libm::pow(self, n)
}
#[inline]
fn sqrt(self) -> Self {
libm::sqrt(self)
}
#[inline]
fn exp(self) -> Self {
libm::exp(self)
}
#[inline]
fn exp2(self) -> Self {
libm::exp2(self)
}
#[inline]
fn ln(self) -> Self {
libm::log(self)
}
#[inline]
fn log(self, base: Self) -> Self {
self.ln() / base.ln()
}
#[inline]
fn log2(self) -> Self {
libm::log2(self)
}
#[inline]
fn log10(self) -> Self {
libm::log10(self)
}
#[inline]
fn cbrt(self) -> Self {
libm::cbrt(self)
}
#[inline]
fn hypot(self, other: Self) -> Self {
libm::hypot(self, other)
}
#[inline]
fn sin(self) -> Self {
libm::sin(self)
}
#[inline]
fn cos(self) -> Self {
libm::cos(self)
}
#[inline]
fn tan(self) -> Self {
libm::tan(self)
}
#[inline]
fn asin(self) -> Self {
libm::asin(self)
}
#[inline]
fn acos(self) -> Self {
libm::acos(self)
}
#[inline]
fn atan(self) -> Self {
libm::atan(self)
}
#[inline]
fn atan2(self, other: Self) -> Self {
libm::atan2(self, other)
}
#[inline]
fn exp_m1(self) -> Self {
libm::expm1(self)
}
#[inline]
fn ln_1p(self) -> Self {
libm::log1p(self)
}
#[inline]
fn sinh(self) -> Self {
libm::sinh(self)
}
#[inline]
fn cosh(self) -> Self {
libm::cosh(self)
}
#[inline]
fn tanh(self) -> Self {
libm::tanh(self)
}
#[inline]
fn asinh(self) -> Self {
let ax = self.abs();
let ix = 1.0 / ax;
(ax + (ax / (Self::hypot(1.0, ix) + ix)))
.ln_1p()
.copysign(self)
}
#[inline]
fn acosh(self) -> Self {
if self < 1.0 {
Self::NAN
} else {
(self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
}
}
#[inline]
fn atanh(self) -> Self {
0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
}
}