core_maths-0.1.1/.cargo_vcs_info.json0000644000000001360000000000100131570ustar { "git": { "sha1": "d8ea96acac3893ad9a7e16cd7526936fbfc51021" }, "path_in_vcs": "" }core_maths-0.1.1/.gitignore000064400000000000000000000000061046102023000137330ustar 00000000000000targetcore_maths-0.1.1/Cargo.toml0000644000000017700000000000100111620ustar # THIS FILE IS AUTOMATICALLY GENERATED BY CARGO # # When uploading crates to the registry Cargo will automatically # "normalize" Cargo.toml files for maximal compatibility # with all versions of Cargo and also rewrite `path` dependencies # to registry (e.g., crates.io) dependencies. # # If you are reading this file be aware that the original Cargo.toml # will likely look very different (and much more reasonable). # See Cargo.toml.orig for the original contents. [package] name = "core_maths" version = "0.1.1" authors = ["Robert Bastian 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(); ``` core_maths-0.1.1/src/lib.rs000064400000000000000000000743151046102023000136640ustar 00000000000000//! 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() } }