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Diffstat (limited to 'library/std/src/f64.rs')
| -rw-r--r-- | library/std/src/f64.rs | 1697 |
1 files changed, 1697 insertions, 0 deletions
diff --git a/library/std/src/f64.rs b/library/std/src/f64.rs new file mode 100644 index 00000000000..f09fc8d790b --- /dev/null +++ b/library/std/src/f64.rs @@ -0,0 +1,1697 @@ +//! This module provides constants which are specific to the implementation +//! of the `f64` floating point data type. +//! +//! *[See also the `f64` primitive type](../../std/primitive.f64.html).* +//! +//! Mathematically significant numbers are provided in the `consts` sub-module. +//! +//! Although using these constants won’t cause compilation warnings, +//! new code should use the associated constants directly on the primitive type. + +#![stable(feature = "rust1", since = "1.0.0")] +#![allow(missing_docs)] + +#[cfg(not(test))] +use crate::intrinsics; +#[cfg(not(test))] +use crate::sys::cmath; + +#[stable(feature = "rust1", since = "1.0.0")] +pub use core::f64::consts; +#[stable(feature = "rust1", since = "1.0.0")] +pub use core::f64::{DIGITS, EPSILON, MANTISSA_DIGITS, RADIX}; +#[stable(feature = "rust1", since = "1.0.0")] +pub use core::f64::{INFINITY, MAX_10_EXP, NAN, NEG_INFINITY}; +#[stable(feature = "rust1", since = "1.0.0")] +pub use core::f64::{MAX, MIN, MIN_POSITIVE}; +#[stable(feature = "rust1", since = "1.0.0")] +pub use core::f64::{MAX_EXP, MIN_10_EXP, MIN_EXP}; + +#[cfg(not(test))] +#[lang = "f64_runtime"] +impl f64 { + /// Returns the largest integer less than or equal to a number. + /// + /// # Examples + /// + /// ``` + /// let f = 3.7_f64; + /// let g = 3.0_f64; + /// let h = -3.7_f64; + /// + /// assert_eq!(f.floor(), 3.0); + /// assert_eq!(g.floor(), 3.0); + /// assert_eq!(h.floor(), -4.0); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn floor(self) -> f64 { + unsafe { intrinsics::floorf64(self) } + } + + /// Returns the smallest integer greater than or equal to a number. + /// + /// # Examples + /// + /// ``` + /// let f = 3.01_f64; + /// let g = 4.0_f64; + /// + /// assert_eq!(f.ceil(), 4.0); + /// assert_eq!(g.ceil(), 4.0); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn ceil(self) -> f64 { + unsafe { intrinsics::ceilf64(self) } + } + + /// Returns the nearest integer to a number. Round half-way cases away from + /// `0.0`. + /// + /// # Examples + /// + /// ``` + /// let f = 3.3_f64; + /// let g = -3.3_f64; + /// + /// assert_eq!(f.round(), 3.0); + /// assert_eq!(g.round(), -3.0); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn round(self) -> f64 { + unsafe { intrinsics::roundf64(self) } + } + + /// Returns the integer part of a number. + /// + /// # Examples + /// + /// ``` + /// let f = 3.7_f64; + /// let g = 3.0_f64; + /// let h = -3.7_f64; + /// + /// assert_eq!(f.trunc(), 3.0); + /// assert_eq!(g.trunc(), 3.0); + /// assert_eq!(h.trunc(), -3.0); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn trunc(self) -> f64 { + unsafe { intrinsics::truncf64(self) } + } + + /// Returns the fractional part of a number. + /// + /// # Examples + /// + /// ``` + /// let x = 3.6_f64; + /// let y = -3.6_f64; + /// let abs_difference_x = (x.fract() - 0.6).abs(); + /// let abs_difference_y = (y.fract() - (-0.6)).abs(); + /// + /// assert!(abs_difference_x < 1e-10); + /// assert!(abs_difference_y < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn fract(self) -> f64 { + self - self.trunc() + } + + /// Computes the absolute value of `self`. Returns `NAN` if the + /// number is `NAN`. + /// + /// # Examples + /// + /// ``` + /// let x = 3.5_f64; + /// let y = -3.5_f64; + /// + /// 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()); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn abs(self) -> f64 { + unsafe { intrinsics::fabsf64(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` + /// + /// # Examples + /// + /// ``` + /// let f = 3.5_f64; + /// + /// assert_eq!(f.signum(), 1.0); + /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0); + /// + /// assert!(f64::NAN.signum().is_nan()); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn signum(self) -> f64 { + if self.is_nan() { Self::NAN } else { 1.0_f64.copysign(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 of + /// `sign` is returned. + /// + /// # Examples + /// + /// ``` + /// let f = 3.5_f64; + /// + /// assert_eq!(f.copysign(0.42), 3.5_f64); + /// assert_eq!(f.copysign(-0.42), -3.5_f64); + /// assert_eq!((-f).copysign(0.42), 3.5_f64); + /// assert_eq!((-f).copysign(-0.42), -3.5_f64); + /// + /// assert!(f64::NAN.copysign(1.0).is_nan()); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "copysign", since = "1.35.0")] + #[inline] + pub fn copysign(self, sign: f64) -> f64 { + unsafe { intrinsics::copysignf64(self, sign) } + } + + /// 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. + /// + /// # Examples + /// + /// ``` + /// let m = 10.0_f64; + /// let x = 4.0_f64; + /// let b = 60.0_f64; + /// + /// // 100.0 + /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn mul_add(self, a: f64, b: f64) -> f64 { + unsafe { intrinsics::fmaf64(self, a, b) } + } + + /// 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`. + /// + /// # Examples + /// + /// ``` + /// let a: f64 = 7.0; + /// let b = 4.0; + /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0 + /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0 + /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0 + /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0 + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[inline] + #[stable(feature = "euclidean_division", since = "1.38.0")] + pub fn div_euclid(self, rhs: f64) -> f64 { + let q = (self / rhs).trunc(); + if self % rhs < 0.0 { + return if rhs > 0.0 { q - 1.0 } else { q + 1.0 }; + } + q + } + + /// 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)` + /// approximatively. + /// + /// # Examples + /// + /// ``` + /// let a: f64 = 7.0; + /// let b = 4.0; + /// assert_eq!(a.rem_euclid(b), 3.0); + /// assert_eq!((-a).rem_euclid(b), 1.0); + /// assert_eq!(a.rem_euclid(-b), 3.0); + /// assert_eq!((-a).rem_euclid(-b), 1.0); + /// // limitation due to round-off error + /// assert!((-f64::EPSILON).rem_euclid(3.0) != 0.0); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[inline] + #[stable(feature = "euclidean_division", since = "1.38.0")] + pub fn rem_euclid(self, rhs: f64) -> f64 { + let r = self % rhs; + if r < 0.0 { r + rhs.abs() } else { r } + } + + /// Raises a number to an integer power. + /// + /// Using this function is generally faster than using `powf` + /// + /// # Examples + /// + /// ``` + /// let x = 2.0_f64; + /// let abs_difference = (x.powi(2) - (x * x)).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn powi(self, n: i32) -> f64 { + unsafe { intrinsics::powif64(self, n) } + } + + /// Raises a number to a floating point power. + /// + /// # Examples + /// + /// ``` + /// let x = 2.0_f64; + /// let abs_difference = (x.powf(2.0) - (x * x)).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn powf(self, n: f64) -> f64 { + unsafe { intrinsics::powf64(self, n) } + } + + /// Returns the square root of a number. + /// + /// Returns NaN if `self` is a negative number. + /// + /// # Examples + /// + /// ``` + /// let positive = 4.0_f64; + /// let negative = -4.0_f64; + /// + /// let abs_difference = (positive.sqrt() - 2.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// assert!(negative.sqrt().is_nan()); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn sqrt(self) -> f64 { + unsafe { intrinsics::sqrtf64(self) } + } + + /// Returns `e^(self)`, (the exponential function). + /// + /// # Examples + /// + /// ``` + /// let one = 1.0_f64; + /// // e^1 + /// let e = one.exp(); + /// + /// // ln(e) - 1 == 0 + /// let abs_difference = (e.ln() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn exp(self) -> f64 { + unsafe { intrinsics::expf64(self) } + } + + /// Returns `2^(self)`. + /// + /// # Examples + /// + /// ``` + /// let f = 2.0_f64; + /// + /// // 2^2 - 4 == 0 + /// let abs_difference = (f.exp2() - 4.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn exp2(self) -> f64 { + unsafe { intrinsics::exp2f64(self) } + } + + /// Returns the natural logarithm of the number. + /// + /// # Examples + /// + /// ``` + /// let one = 1.0_f64; + /// // e^1 + /// let e = one.exp(); + /// + /// // ln(e) - 1 == 0 + /// let abs_difference = (e.ln() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn ln(self) -> f64 { + self.log_wrapper(|n| unsafe { intrinsics::logf64(n) }) + } + + /// Returns the logarithm of the number with respect to an arbitrary base. + /// + /// The result may 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. + /// + /// # Examples + /// + /// ``` + /// let twenty_five = 25.0_f64; + /// + /// // log5(25) - 2 == 0 + /// let abs_difference = (twenty_five.log(5.0) - 2.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn log(self, base: f64) -> f64 { + self.ln() / base.ln() + } + + /// Returns the base 2 logarithm of the number. + /// + /// # Examples + /// + /// ``` + /// let four = 4.0_f64; + /// + /// // log2(4) - 2 == 0 + /// let abs_difference = (four.log2() - 2.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn log2(self) -> f64 { + self.log_wrapper(|n| { + #[cfg(target_os = "android")] + return crate::sys::android::log2f64(n); + #[cfg(not(target_os = "android"))] + return unsafe { intrinsics::log2f64(n) }; + }) + } + + /// Returns the base 10 logarithm of the number. + /// + /// # Examples + /// + /// ``` + /// let hundred = 100.0_f64; + /// + /// // log10(100) - 2 == 0 + /// let abs_difference = (hundred.log10() - 2.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn log10(self) -> f64 { + self.log_wrapper(|n| unsafe { intrinsics::log10f64(n) }) + } + + /// The positive difference of two numbers. + /// + /// * If `self <= other`: `0:0` + /// * Else: `self - other` + /// + /// # Examples + /// + /// ``` + /// let x = 3.0_f64; + /// let y = -3.0_f64; + /// + /// 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); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + #[rustc_deprecated( + since = "1.10.0", + reason = "you probably meant `(self - other).abs()`: \ + this operation is `(self - other).max(0.0)` \ + except that `abs_sub` also propagates NaNs (also \ + known as `fdim` in C). If you truly need the positive \ + difference, consider using that expression or the C function \ + `fdim`, depending on how you wish to handle NaN (please consider \ + filing an issue describing your use-case too)." + )] + pub fn abs_sub(self, other: f64) -> f64 { + unsafe { cmath::fdim(self, other) } + } + + /// Returns the cubic root of a number. + /// + /// # Examples + /// + /// ``` + /// let x = 8.0_f64; + /// + /// // x^(1/3) - 2 == 0 + /// let abs_difference = (x.cbrt() - 2.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn cbrt(self) -> f64 { + unsafe { cmath::cbrt(self) } + } + + /// Calculates the length of the hypotenuse of a right-angle triangle given + /// legs of length `x` and `y`. + /// + /// # Examples + /// + /// ``` + /// let x = 2.0_f64; + /// let y = 3.0_f64; + /// + /// // sqrt(x^2 + y^2) + /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn hypot(self, other: f64) -> f64 { + unsafe { cmath::hypot(self, other) } + } + + /// Computes the sine of a number (in radians). + /// + /// # Examples + /// + /// ``` + /// let x = std::f64::consts::FRAC_PI_2; + /// + /// let abs_difference = (x.sin() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn sin(self) -> f64 { + unsafe { intrinsics::sinf64(self) } + } + + /// Computes the cosine of a number (in radians). + /// + /// # Examples + /// + /// ``` + /// let x = 2.0 * std::f64::consts::PI; + /// + /// let abs_difference = (x.cos() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn cos(self) -> f64 { + unsafe { intrinsics::cosf64(self) } + } + + /// Computes the tangent of a number (in radians). + /// + /// # Examples + /// + /// ``` + /// let x = std::f64::consts::FRAC_PI_4; + /// let abs_difference = (x.tan() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-14); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn tan(self) -> f64 { + unsafe { cmath::tan(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]. + /// + /// # Examples + /// + /// ``` + /// let f = std::f64::consts::FRAC_PI_2; + /// + /// // asin(sin(pi/2)) + /// let abs_difference = (f.sin().asin() - std::f64::consts::FRAC_PI_2).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn asin(self) -> f64 { + unsafe { cmath::asin(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]. + /// + /// # Examples + /// + /// ``` + /// let f = std::f64::consts::FRAC_PI_4; + /// + /// // acos(cos(pi/4)) + /// let abs_difference = (f.cos().acos() - std::f64::consts::FRAC_PI_4).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn acos(self) -> f64 { + unsafe { cmath::acos(self) } + } + + /// Computes the arctangent of a number. Return value is in radians in the + /// range [-pi/2, pi/2]; + /// + /// # Examples + /// + /// ``` + /// let f = 1.0_f64; + /// + /// // atan(tan(1)) + /// let abs_difference = (f.tan().atan() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn atan(self) -> f64 { + unsafe { cmath::atan(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)` + /// + /// # Examples + /// + /// ``` + /// // 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 = (y1.atan2(x1) - (-std::f64::consts::FRAC_PI_4)).abs(); + /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f64::consts::FRAC_PI_4)).abs(); + /// + /// assert!(abs_difference_1 < 1e-10); + /// assert!(abs_difference_2 < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn atan2(self, other: f64) -> f64 { + unsafe { cmath::atan2(self, other) } + } + + /// Simultaneously computes the sine and cosine of the number, `x`. Returns + /// `(sin(x), cos(x))`. + /// + /// # Examples + /// + /// ``` + /// let x = std::f64::consts::FRAC_PI_4; + /// 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_1 < 1e-10); + /// ``` + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn sin_cos(self) -> (f64, f64) { + (self.sin(), self.cos()) + } + + /// Returns `e^(self) - 1` in a way that is accurate even if the + /// number is close to zero. + /// + /// # Examples + /// + /// ``` + /// let x = 7.0_f64; + /// + /// // e^(ln(7)) - 1 + /// let abs_difference = (x.ln().exp_m1() - 6.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn exp_m1(self) -> f64 { + unsafe { cmath::expm1(self) } + } + + /// Returns `ln(1+n)` (natural logarithm) more accurately than if + /// the operations were performed separately. + /// + /// # Examples + /// + /// ``` + /// let x = std::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); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn ln_1p(self) -> f64 { + unsafe { cmath::log1p(self) } + } + + /// Hyperbolic sine function. + /// + /// # Examples + /// + /// ``` + /// let e = std::f64::consts::E; + /// let x = 1.0_f64; + /// + /// 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); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn sinh(self) -> f64 { + unsafe { cmath::sinh(self) } + } + + /// Hyperbolic cosine function. + /// + /// # Examples + /// + /// ``` + /// let e = std::f64::consts::E; + /// let x = 1.0_f64; + /// 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); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn cosh(self) -> f64 { + unsafe { cmath::cosh(self) } + } + + /// Hyperbolic tangent function. + /// + /// # Examples + /// + /// ``` + /// let e = std::f64::consts::E; + /// let x = 1.0_f64; + /// + /// 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); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn tanh(self) -> f64 { + unsafe { cmath::tanh(self) } + } + + /// Inverse hyperbolic sine function. + /// + /// # Examples + /// + /// ``` + /// let x = 1.0_f64; + /// let f = x.sinh().asinh(); + /// + /// let abs_difference = (f - x).abs(); + /// + /// assert!(abs_difference < 1.0e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn asinh(self) -> f64 { + (self.abs() + ((self * self) + 1.0).sqrt()).ln().copysign(self) + } + + /// Inverse hyperbolic cosine function. + /// + /// # Examples + /// + /// ``` + /// let x = 1.0_f64; + /// let f = x.cosh().acosh(); + /// + /// let abs_difference = (f - x).abs(); + /// + /// assert!(abs_difference < 1.0e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn acosh(self) -> f64 { + if self < 1.0 { Self::NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() } + } + + /// Inverse hyperbolic tangent function. + /// + /// # Examples + /// + /// ``` + /// let e = std::f64::consts::E; + /// let f = e.tanh().atanh(); + /// + /// let abs_difference = (f - e).abs(); + /// + /// assert!(abs_difference < 1.0e-10); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn atanh(self) -> f64 { + 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p() + } + + /// Restrict a value to a certain interval unless it is NaN. + /// + /// Returns `max` if `self` is greater than `max`, and `min` if `self` is + /// less than `min`. Otherwise this returns `self`. + /// + /// Note that this function returns NaN if the initial value was NaN as + /// well. + /// + /// # Panics + /// + /// Panics if `min > max`, `min` is NaN, or `max` is NaN. + /// + /// # Examples + /// + /// ``` + /// #![feature(clamp)] + /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0); + /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0); + /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0); + /// assert!((f64::NAN).clamp(-2.0, 1.0).is_nan()); + /// ``` + #[must_use = "method returns a new number and does not mutate the original value"] + #[unstable(feature = "clamp", issue = "44095")] + #[inline] + pub fn clamp(self, min: f64, max: f64) -> f64 { + assert!(min <= max); + let mut x = self; + if x < min { + x = min; + } + if x > max { + x = max; + } + x + } + + // Solaris/Illumos requires a wrapper around log, log2, and log10 functions + // because of their non-standard behavior (e.g., log(-n) returns -Inf instead + // of expected NaN). + fn log_wrapper<F: Fn(f64) -> f64>(self, log_fn: F) -> f64 { + if !cfg!(any(target_os = "solaris", target_os = "illumos")) { + log_fn(self) + } else { + if self.is_finite() { + if self > 0.0 { + log_fn(self) + } else if self == 0.0 { + Self::NEG_INFINITY // log(0) = -Inf + } else { + Self::NAN // log(-n) = NaN + } + } else if self.is_nan() { + self // log(NaN) = NaN + } else if self > 0.0 { + self // log(Inf) = Inf + } else { + Self::NAN // log(-Inf) = NaN + } + } + } +} + +#[cfg(test)] +mod tests { + use crate::f64::consts; + use crate::num::FpCategory as Fp; + use crate::num::*; + + #[test] + fn test_num_f64() { + test_num(10f64, 2f64); + } + + #[test] + fn test_min_nan() { + assert_eq!(f64::NAN.min(2.0), 2.0); + assert_eq!(2.0f64.min(f64::NAN), 2.0); + } + + #[test] + fn test_max_nan() { + assert_eq!(f64::NAN.max(2.0), 2.0); + assert_eq!(2.0f64.max(f64::NAN), 2.0); + } + + #[test] + fn test_nan() { + let nan: f64 = f64::NAN; + assert!(nan.is_nan()); + assert!(!nan.is_infinite()); + assert!(!nan.is_finite()); + assert!(!nan.is_normal()); + assert!(nan.is_sign_positive()); + assert!(!nan.is_sign_negative()); + assert_eq!(Fp::Nan, nan.classify()); + } + + #[test] + fn test_infinity() { + let inf: f64 = f64::INFINITY; + assert!(inf.is_infinite()); + assert!(!inf.is_finite()); + assert!(inf.is_sign_positive()); + assert!(!inf.is_sign_negative()); + assert!(!inf.is_nan()); + assert!(!inf.is_normal()); + assert_eq!(Fp::Infinite, inf.classify()); + } + + #[test] + fn test_neg_infinity() { + let neg_inf: f64 = f64::NEG_INFINITY; + assert!(neg_inf.is_infinite()); + assert!(!neg_inf.is_finite()); + assert!(!neg_inf.is_sign_positive()); + assert!(neg_inf.is_sign_negative()); + assert!(!neg_inf.is_nan()); + assert!(!neg_inf.is_normal()); + assert_eq!(Fp::Infinite, neg_inf.classify()); + } + + #[test] + fn test_zero() { + let zero: f64 = 0.0f64; + assert_eq!(0.0, zero); + assert!(!zero.is_infinite()); + assert!(zero.is_finite()); + assert!(zero.is_sign_positive()); + assert!(!zero.is_sign_negative()); + assert!(!zero.is_nan()); + assert!(!zero.is_normal()); + assert_eq!(Fp::Zero, zero.classify()); + } + + #[test] + fn test_neg_zero() { + let neg_zero: f64 = -0.0; + assert_eq!(0.0, neg_zero); + assert!(!neg_zero.is_infinite()); + assert!(neg_zero.is_finite()); + assert!(!neg_zero.is_sign_positive()); + assert!(neg_zero.is_sign_negative()); + assert!(!neg_zero.is_nan()); + assert!(!neg_zero.is_normal()); + assert_eq!(Fp::Zero, neg_zero.classify()); + } + + #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630 + #[test] + fn test_one() { + let one: f64 = 1.0f64; + assert_eq!(1.0, one); + assert!(!one.is_infinite()); + assert!(one.is_finite()); + assert!(one.is_sign_positive()); + assert!(!one.is_sign_negative()); + assert!(!one.is_nan()); + assert!(one.is_normal()); + assert_eq!(Fp::Normal, one.classify()); + } + + #[test] + fn test_is_nan() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert!(nan.is_nan()); + assert!(!0.0f64.is_nan()); + assert!(!5.3f64.is_nan()); + assert!(!(-10.732f64).is_nan()); + assert!(!inf.is_nan()); + assert!(!neg_inf.is_nan()); + } + + #[test] + fn test_is_infinite() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert!(!nan.is_infinite()); + assert!(inf.is_infinite()); + assert!(neg_inf.is_infinite()); + assert!(!0.0f64.is_infinite()); + assert!(!42.8f64.is_infinite()); + assert!(!(-109.2f64).is_infinite()); + } + + #[test] + fn test_is_finite() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert!(!nan.is_finite()); + assert!(!inf.is_finite()); + assert!(!neg_inf.is_finite()); + assert!(0.0f64.is_finite()); + assert!(42.8f64.is_finite()); + assert!((-109.2f64).is_finite()); + } + + #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630 + #[test] + fn test_is_normal() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + let zero: f64 = 0.0f64; + let neg_zero: f64 = -0.0; + assert!(!nan.is_normal()); + assert!(!inf.is_normal()); + assert!(!neg_inf.is_normal()); + assert!(!zero.is_normal()); + assert!(!neg_zero.is_normal()); + assert!(1f64.is_normal()); + assert!(1e-307f64.is_normal()); + assert!(!1e-308f64.is_normal()); + } + + #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630 + #[test] + fn test_classify() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + let zero: f64 = 0.0f64; + let neg_zero: f64 = -0.0; + assert_eq!(nan.classify(), Fp::Nan); + assert_eq!(inf.classify(), Fp::Infinite); + assert_eq!(neg_inf.classify(), Fp::Infinite); + assert_eq!(zero.classify(), Fp::Zero); + assert_eq!(neg_zero.classify(), Fp::Zero); + assert_eq!(1e-307f64.classify(), Fp::Normal); + assert_eq!(1e-308f64.classify(), Fp::Subnormal); + } + + #[test] + fn test_floor() { + assert_approx_eq!(1.0f64.floor(), 1.0f64); + assert_approx_eq!(1.3f64.floor(), 1.0f64); + assert_approx_eq!(1.5f64.floor(), 1.0f64); + assert_approx_eq!(1.7f64.floor(), 1.0f64); + assert_approx_eq!(0.0f64.floor(), 0.0f64); + assert_approx_eq!((-0.0f64).floor(), -0.0f64); + assert_approx_eq!((-1.0f64).floor(), -1.0f64); + assert_approx_eq!((-1.3f64).floor(), -2.0f64); + assert_approx_eq!((-1.5f64).floor(), -2.0f64); + assert_approx_eq!((-1.7f64).floor(), -2.0f64); + } + + #[test] + fn test_ceil() { + assert_approx_eq!(1.0f64.ceil(), 1.0f64); + assert_approx_eq!(1.3f64.ceil(), 2.0f64); + assert_approx_eq!(1.5f64.ceil(), 2.0f64); + assert_approx_eq!(1.7f64.ceil(), 2.0f64); + assert_approx_eq!(0.0f64.ceil(), 0.0f64); + assert_approx_eq!((-0.0f64).ceil(), -0.0f64); + assert_approx_eq!((-1.0f64).ceil(), -1.0f64); + assert_approx_eq!((-1.3f64).ceil(), -1.0f64); + assert_approx_eq!((-1.5f64).ceil(), -1.0f64); + assert_approx_eq!((-1.7f64).ceil(), -1.0f64); + } + + #[test] + fn test_round() { + assert_approx_eq!(1.0f64.round(), 1.0f64); + assert_approx_eq!(1.3f64.round(), 1.0f64); + assert_approx_eq!(1.5f64.round(), 2.0f64); + assert_approx_eq!(1.7f64.round(), 2.0f64); + assert_approx_eq!(0.0f64.round(), 0.0f64); + assert_approx_eq!((-0.0f64).round(), -0.0f64); + assert_approx_eq!((-1.0f64).round(), -1.0f64); + assert_approx_eq!((-1.3f64).round(), -1.0f64); + assert_approx_eq!((-1.5f64).round(), -2.0f64); + assert_approx_eq!((-1.7f64).round(), -2.0f64); + } + + #[test] + fn test_trunc() { + assert_approx_eq!(1.0f64.trunc(), 1.0f64); + assert_approx_eq!(1.3f64.trunc(), 1.0f64); + assert_approx_eq!(1.5f64.trunc(), 1.0f64); + assert_approx_eq!(1.7f64.trunc(), 1.0f64); + assert_approx_eq!(0.0f64.trunc(), 0.0f64); + assert_approx_eq!((-0.0f64).trunc(), -0.0f64); + assert_approx_eq!((-1.0f64).trunc(), -1.0f64); + assert_approx_eq!((-1.3f64).trunc(), -1.0f64); + assert_approx_eq!((-1.5f64).trunc(), -1.0f64); + assert_approx_eq!((-1.7f64).trunc(), -1.0f64); + } + + #[test] + fn test_fract() { + assert_approx_eq!(1.0f64.fract(), 0.0f64); + assert_approx_eq!(1.3f64.fract(), 0.3f64); + assert_approx_eq!(1.5f64.fract(), 0.5f64); + assert_approx_eq!(1.7f64.fract(), 0.7f64); + assert_approx_eq!(0.0f64.fract(), 0.0f64); + assert_approx_eq!((-0.0f64).fract(), -0.0f64); + assert_approx_eq!((-1.0f64).fract(), -0.0f64); + assert_approx_eq!((-1.3f64).fract(), -0.3f64); + assert_approx_eq!((-1.5f64).fract(), -0.5f64); + assert_approx_eq!((-1.7f64).fract(), -0.7f64); + } + + #[test] + fn test_abs() { + assert_eq!(f64::INFINITY.abs(), f64::INFINITY); + assert_eq!(1f64.abs(), 1f64); + assert_eq!(0f64.abs(), 0f64); + assert_eq!((-0f64).abs(), 0f64); + assert_eq!((-1f64).abs(), 1f64); + assert_eq!(f64::NEG_INFINITY.abs(), f64::INFINITY); + assert_eq!((1f64 / f64::NEG_INFINITY).abs(), 0f64); + assert!(f64::NAN.abs().is_nan()); + } + + #[test] + fn test_signum() { + assert_eq!(f64::INFINITY.signum(), 1f64); + assert_eq!(1f64.signum(), 1f64); + assert_eq!(0f64.signum(), 1f64); + assert_eq!((-0f64).signum(), -1f64); + assert_eq!((-1f64).signum(), -1f64); + assert_eq!(f64::NEG_INFINITY.signum(), -1f64); + assert_eq!((1f64 / f64::NEG_INFINITY).signum(), -1f64); + assert!(f64::NAN.signum().is_nan()); + } + + #[test] + fn test_is_sign_positive() { + assert!(f64::INFINITY.is_sign_positive()); + assert!(1f64.is_sign_positive()); + assert!(0f64.is_sign_positive()); + assert!(!(-0f64).is_sign_positive()); + assert!(!(-1f64).is_sign_positive()); + assert!(!f64::NEG_INFINITY.is_sign_positive()); + assert!(!(1f64 / f64::NEG_INFINITY).is_sign_positive()); + assert!(f64::NAN.is_sign_positive()); + assert!(!(-f64::NAN).is_sign_positive()); + } + + #[test] + fn test_is_sign_negative() { + assert!(!f64::INFINITY.is_sign_negative()); + assert!(!1f64.is_sign_negative()); + assert!(!0f64.is_sign_negative()); + assert!((-0f64).is_sign_negative()); + assert!((-1f64).is_sign_negative()); + assert!(f64::NEG_INFINITY.is_sign_negative()); + assert!((1f64 / f64::NEG_INFINITY).is_sign_negative()); + assert!(!f64::NAN.is_sign_negative()); + assert!((-f64::NAN).is_sign_negative()); + } + + #[test] + fn test_mul_add() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05); + assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65); + assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2); + assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6); + assert!(nan.mul_add(7.8, 9.0).is_nan()); + assert_eq!(inf.mul_add(7.8, 9.0), inf); + assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf); + assert_eq!(8.9f64.mul_add(inf, 3.2), inf); + assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf); + } + + #[test] + fn test_recip() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert_eq!(1.0f64.recip(), 1.0); + assert_eq!(2.0f64.recip(), 0.5); + assert_eq!((-0.4f64).recip(), -2.5); + assert_eq!(0.0f64.recip(), inf); + assert!(nan.recip().is_nan()); + assert_eq!(inf.recip(), 0.0); + assert_eq!(neg_inf.recip(), 0.0); + } + + #[test] + fn test_powi() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert_eq!(1.0f64.powi(1), 1.0); + assert_approx_eq!((-3.1f64).powi(2), 9.61); + assert_approx_eq!(5.9f64.powi(-2), 0.028727); + assert_eq!(8.3f64.powi(0), 1.0); + assert!(nan.powi(2).is_nan()); + assert_eq!(inf.powi(3), inf); + assert_eq!(neg_inf.powi(2), inf); + } + + #[test] + fn test_powf() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert_eq!(1.0f64.powf(1.0), 1.0); + assert_approx_eq!(3.4f64.powf(4.5), 246.408183); + assert_approx_eq!(2.7f64.powf(-3.2), 0.041652); + assert_approx_eq!((-3.1f64).powf(2.0), 9.61); + assert_approx_eq!(5.9f64.powf(-2.0), 0.028727); + assert_eq!(8.3f64.powf(0.0), 1.0); + assert!(nan.powf(2.0).is_nan()); + assert_eq!(inf.powf(2.0), inf); + assert_eq!(neg_inf.powf(3.0), neg_inf); + } + + #[test] + fn test_sqrt_domain() { + assert!(f64::NAN.sqrt().is_nan()); + assert!(f64::NEG_INFINITY.sqrt().is_nan()); + assert!((-1.0f64).sqrt().is_nan()); + assert_eq!((-0.0f64).sqrt(), -0.0); + assert_eq!(0.0f64.sqrt(), 0.0); + assert_eq!(1.0f64.sqrt(), 1.0); + assert_eq!(f64::INFINITY.sqrt(), f64::INFINITY); + } + + #[test] + fn test_exp() { + assert_eq!(1.0, 0.0f64.exp()); + assert_approx_eq!(2.718282, 1.0f64.exp()); + assert_approx_eq!(148.413159, 5.0f64.exp()); + + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + let nan: f64 = f64::NAN; + assert_eq!(inf, inf.exp()); + assert_eq!(0.0, neg_inf.exp()); + assert!(nan.exp().is_nan()); + } + + #[test] + fn test_exp2() { + assert_eq!(32.0, 5.0f64.exp2()); + assert_eq!(1.0, 0.0f64.exp2()); + + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + let nan: f64 = f64::NAN; + assert_eq!(inf, inf.exp2()); + assert_eq!(0.0, neg_inf.exp2()); + assert!(nan.exp2().is_nan()); + } + + #[test] + fn test_ln() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert_approx_eq!(1.0f64.exp().ln(), 1.0); + assert!(nan.ln().is_nan()); + assert_eq!(inf.ln(), inf); + assert!(neg_inf.ln().is_nan()); + assert!((-2.3f64).ln().is_nan()); + assert_eq!((-0.0f64).ln(), neg_inf); + assert_eq!(0.0f64.ln(), neg_inf); + assert_approx_eq!(4.0f64.ln(), 1.386294); + } + + #[test] + fn test_log() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert_eq!(10.0f64.log(10.0), 1.0); + assert_approx_eq!(2.3f64.log(3.5), 0.664858); + assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0); + assert!(1.0f64.log(1.0).is_nan()); + assert!(1.0f64.log(-13.9).is_nan()); + assert!(nan.log(2.3).is_nan()); + assert_eq!(inf.log(10.0), inf); + assert!(neg_inf.log(8.8).is_nan()); + assert!((-2.3f64).log(0.1).is_nan()); + assert_eq!((-0.0f64).log(2.0), neg_inf); + assert_eq!(0.0f64.log(7.0), neg_inf); + } + + #[test] + fn test_log2() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert_approx_eq!(10.0f64.log2(), 3.321928); + assert_approx_eq!(2.3f64.log2(), 1.201634); + assert_approx_eq!(1.0f64.exp().log2(), 1.442695); + assert!(nan.log2().is_nan()); + assert_eq!(inf.log2(), inf); + assert!(neg_inf.log2().is_nan()); + assert!((-2.3f64).log2().is_nan()); + assert_eq!((-0.0f64).log2(), neg_inf); + assert_eq!(0.0f64.log2(), neg_inf); + } + + #[test] + fn test_log10() { + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert_eq!(10.0f64.log10(), 1.0); + assert_approx_eq!(2.3f64.log10(), 0.361728); + assert_approx_eq!(1.0f64.exp().log10(), 0.434294); + assert_eq!(1.0f64.log10(), 0.0); + assert!(nan.log10().is_nan()); + assert_eq!(inf.log10(), inf); + assert!(neg_inf.log10().is_nan()); + assert!((-2.3f64).log10().is_nan()); + assert_eq!((-0.0f64).log10(), neg_inf); + assert_eq!(0.0f64.log10(), neg_inf); + } + + #[test] + fn test_to_degrees() { + let pi: f64 = consts::PI; + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert_eq!(0.0f64.to_degrees(), 0.0); + assert_approx_eq!((-5.8f64).to_degrees(), -332.315521); + assert_eq!(pi.to_degrees(), 180.0); + assert!(nan.to_degrees().is_nan()); + assert_eq!(inf.to_degrees(), inf); + assert_eq!(neg_inf.to_degrees(), neg_inf); + } + + #[test] + fn test_to_radians() { + let pi: f64 = consts::PI; + let nan: f64 = f64::NAN; + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + assert_eq!(0.0f64.to_radians(), 0.0); + assert_approx_eq!(154.6f64.to_radians(), 2.698279); + assert_approx_eq!((-332.31f64).to_radians(), -5.799903); + assert_eq!(180.0f64.to_radians(), pi); + assert!(nan.to_radians().is_nan()); + assert_eq!(inf.to_radians(), inf); + assert_eq!(neg_inf.to_radians(), neg_inf); + } + + #[test] + fn test_asinh() { + assert_eq!(0.0f64.asinh(), 0.0f64); + assert_eq!((-0.0f64).asinh(), -0.0f64); + + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + let nan: f64 = f64::NAN; + assert_eq!(inf.asinh(), inf); + assert_eq!(neg_inf.asinh(), neg_inf); + assert!(nan.asinh().is_nan()); + assert!((-0.0f64).asinh().is_sign_negative()); + // issue 63271 + assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64); + assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64); + // regression test for the catastrophic cancellation fixed in 72486 + assert_approx_eq!((-67452098.07139316f64).asinh(), -18.72007542627454439398548429400083); + } + + #[test] + fn test_acosh() { + assert_eq!(1.0f64.acosh(), 0.0f64); + assert!(0.999f64.acosh().is_nan()); + + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + let nan: f64 = f64::NAN; + assert_eq!(inf.acosh(), inf); + assert!(neg_inf.acosh().is_nan()); + assert!(nan.acosh().is_nan()); + assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64); + assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64); + } + + #[test] + fn test_atanh() { + assert_eq!(0.0f64.atanh(), 0.0f64); + assert_eq!((-0.0f64).atanh(), -0.0f64); + + let inf: f64 = f64::INFINITY; + let neg_inf: f64 = f64::NEG_INFINITY; + let nan: f64 = f64::NAN; + assert_eq!(1.0f64.atanh(), inf); + assert_eq!((-1.0f64).atanh(), neg_inf); + assert!(2f64.atanh().atanh().is_nan()); + assert!((-2f64).atanh().atanh().is_nan()); + assert!(inf.atanh().is_nan()); + assert!(neg_inf.atanh().is_nan()); + assert!(nan.atanh().is_nan()); + assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64); + assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64); + } + + #[test] + fn test_real_consts() { + use super::consts; + let pi: f64 = consts::PI; + let frac_pi_2: f64 = consts::FRAC_PI_2; + let frac_pi_3: f64 = consts::FRAC_PI_3; + let frac_pi_4: f64 = consts::FRAC_PI_4; + let frac_pi_6: f64 = consts::FRAC_PI_6; + let frac_pi_8: f64 = consts::FRAC_PI_8; + let frac_1_pi: f64 = consts::FRAC_1_PI; + let frac_2_pi: f64 = consts::FRAC_2_PI; + let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI; + let sqrt2: f64 = consts::SQRT_2; + let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2; + let e: f64 = consts::E; + let log2_e: f64 = consts::LOG2_E; + let log10_e: f64 = consts::LOG10_E; + let ln_2: f64 = consts::LN_2; + let ln_10: f64 = consts::LN_10; + + assert_approx_eq!(frac_pi_2, pi / 2f64); + assert_approx_eq!(frac_pi_3, pi / 3f64); + assert_approx_eq!(frac_pi_4, pi / 4f64); + assert_approx_eq!(frac_pi_6, pi / 6f64); + assert_approx_eq!(frac_pi_8, pi / 8f64); + assert_approx_eq!(frac_1_pi, 1f64 / pi); + assert_approx_eq!(frac_2_pi, 2f64 / pi); + assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt()); + assert_approx_eq!(sqrt2, 2f64.sqrt()); + assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt()); + assert_approx_eq!(log2_e, e.log2()); + assert_approx_eq!(log10_e, e.log10()); + assert_approx_eq!(ln_2, 2f64.ln()); + assert_approx_eq!(ln_10, 10f64.ln()); + } + + #[test] + fn test_float_bits_conv() { + assert_eq!((1f64).to_bits(), 0x3ff0000000000000); + assert_eq!((12.5f64).to_bits(), 0x4029000000000000); + assert_eq!((1337f64).to_bits(), 0x4094e40000000000); + assert_eq!((-14.25f64).to_bits(), 0xc02c800000000000); + assert_approx_eq!(f64::from_bits(0x3ff0000000000000), 1.0); + assert_approx_eq!(f64::from_bits(0x4029000000000000), 12.5); + assert_approx_eq!(f64::from_bits(0x4094e40000000000), 1337.0); + assert_approx_eq!(f64::from_bits(0xc02c800000000000), -14.25); + + // Check that NaNs roundtrip their bits regardless of signaling-ness + // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits + let masked_nan1 = f64::NAN.to_bits() ^ 0x000A_AAAA_AAAA_AAAA; + let masked_nan2 = f64::NAN.to_bits() ^ 0x0005_5555_5555_5555; + assert!(f64::from_bits(masked_nan1).is_nan()); + assert!(f64::from_bits(masked_nan2).is_nan()); + + assert_eq!(f64::from_bits(masked_nan1).to_bits(), masked_nan1); + assert_eq!(f64::from_bits(masked_nan2).to_bits(), masked_nan2); + } + + #[test] + #[should_panic] + fn test_clamp_min_greater_than_max() { + let _ = 1.0f64.clamp(3.0, 1.0); + } + + #[test] + #[should_panic] + fn test_clamp_min_is_nan() { + let _ = 1.0f64.clamp(f64::NAN, 1.0); + } + + #[test] + #[should_panic] + fn test_clamp_max_is_nan() { + let _ = 1.0f64.clamp(3.0, f64::NAN); + } + + #[test] + fn test_total_cmp() { + use core::cmp::Ordering; + + fn quiet_bit_mask() -> u64 { + 1 << (f64::MANTISSA_DIGITS - 2) + } + + fn min_subnorm() -> f64 { + f64::MIN_POSITIVE / f64::powf(2.0, f64::MANTISSA_DIGITS as f64 - 1.0) + } + + fn max_subnorm() -> f64 { + f64::MIN_POSITIVE - min_subnorm() + } + + fn q_nan() -> f64 { + f64::from_bits(f64::NAN.to_bits() | quiet_bit_mask()) + } + + fn s_nan() -> f64 { + f64::from_bits((f64::NAN.to_bits() & !quiet_bit_mask()) + 42) + } + + assert_eq!(Ordering::Equal, (-q_nan()).total_cmp(&-q_nan())); + assert_eq!(Ordering::Equal, (-s_nan()).total_cmp(&-s_nan())); + assert_eq!(Ordering::Equal, (-f64::INFINITY).total_cmp(&-f64::INFINITY)); + assert_eq!(Ordering::Equal, (-f64::MAX).total_cmp(&-f64::MAX)); + assert_eq!(Ordering::Equal, (-2.5_f64).total_cmp(&-2.5)); + assert_eq!(Ordering::Equal, (-1.0_f64).total_cmp(&-1.0)); + assert_eq!(Ordering::Equal, (-1.5_f64).total_cmp(&-1.5)); + assert_eq!(Ordering::Equal, (-0.5_f64).total_cmp(&-0.5)); + assert_eq!(Ordering::Equal, (-f64::MIN_POSITIVE).total_cmp(&-f64::MIN_POSITIVE)); + assert_eq!(Ordering::Equal, (-max_subnorm()).total_cmp(&-max_subnorm())); + assert_eq!(Ordering::Equal, (-min_subnorm()).total_cmp(&-min_subnorm())); + assert_eq!(Ordering::Equal, (-0.0_f64).total_cmp(&-0.0)); + assert_eq!(Ordering::Equal, 0.0_f64.total_cmp(&0.0)); + assert_eq!(Ordering::Equal, min_subnorm().total_cmp(&min_subnorm())); + assert_eq!(Ordering::Equal, max_subnorm().total_cmp(&max_subnorm())); + assert_eq!(Ordering::Equal, f64::MIN_POSITIVE.total_cmp(&f64::MIN_POSITIVE)); + assert_eq!(Ordering::Equal, 0.5_f64.total_cmp(&0.5)); + assert_eq!(Ordering::Equal, 1.0_f64.total_cmp(&1.0)); + assert_eq!(Ordering::Equal, 1.5_f64.total_cmp(&1.5)); + assert_eq!(Ordering::Equal, 2.5_f64.total_cmp(&2.5)); + assert_eq!(Ordering::Equal, f64::MAX.total_cmp(&f64::MAX)); + assert_eq!(Ordering::Equal, f64::INFINITY.total_cmp(&f64::INFINITY)); + assert_eq!(Ordering::Equal, s_nan().total_cmp(&s_nan())); + assert_eq!(Ordering::Equal, q_nan().total_cmp(&q_nan())); + + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-s_nan())); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::INFINITY)); + assert_eq!(Ordering::Less, (-f64::INFINITY).total_cmp(&-f64::MAX)); + assert_eq!(Ordering::Less, (-f64::MAX).total_cmp(&-2.5)); + assert_eq!(Ordering::Less, (-2.5_f64).total_cmp(&-1.5)); + assert_eq!(Ordering::Less, (-1.5_f64).total_cmp(&-1.0)); + assert_eq!(Ordering::Less, (-1.0_f64).total_cmp(&-0.5)); + assert_eq!(Ordering::Less, (-0.5_f64).total_cmp(&-f64::MIN_POSITIVE)); + assert_eq!(Ordering::Less, (-f64::MIN_POSITIVE).total_cmp(&-max_subnorm())); + assert_eq!(Ordering::Less, (-max_subnorm()).total_cmp(&-min_subnorm())); + assert_eq!(Ordering::Less, (-min_subnorm()).total_cmp(&-0.0)); + assert_eq!(Ordering::Less, (-0.0_f64).total_cmp(&0.0)); + assert_eq!(Ordering::Less, 0.0_f64.total_cmp(&min_subnorm())); + assert_eq!(Ordering::Less, min_subnorm().total_cmp(&max_subnorm())); + assert_eq!(Ordering::Less, max_subnorm().total_cmp(&f64::MIN_POSITIVE)); + assert_eq!(Ordering::Less, f64::MIN_POSITIVE.total_cmp(&0.5)); + assert_eq!(Ordering::Less, 0.5_f64.total_cmp(&1.0)); + assert_eq!(Ordering::Less, 1.0_f64.total_cmp(&1.5)); + assert_eq!(Ordering::Less, 1.5_f64.total_cmp(&2.5)); + assert_eq!(Ordering::Less, 2.5_f64.total_cmp(&f64::MAX)); + assert_eq!(Ordering::Less, f64::MAX.total_cmp(&f64::INFINITY)); + assert_eq!(Ordering::Less, f64::INFINITY.total_cmp(&s_nan())); + assert_eq!(Ordering::Less, s_nan().total_cmp(&q_nan())); + + assert_eq!(Ordering::Greater, (-s_nan()).total_cmp(&-q_nan())); + assert_eq!(Ordering::Greater, (-f64::INFINITY).total_cmp(&-s_nan())); + assert_eq!(Ordering::Greater, (-f64::MAX).total_cmp(&-f64::INFINITY)); + assert_eq!(Ordering::Greater, (-2.5_f64).total_cmp(&-f64::MAX)); + assert_eq!(Ordering::Greater, (-1.5_f64).total_cmp(&-2.5)); + assert_eq!(Ordering::Greater, (-1.0_f64).total_cmp(&-1.5)); + assert_eq!(Ordering::Greater, (-0.5_f64).total_cmp(&-1.0)); + assert_eq!(Ordering::Greater, (-f64::MIN_POSITIVE).total_cmp(&-0.5)); + assert_eq!(Ordering::Greater, (-max_subnorm()).total_cmp(&-f64::MIN_POSITIVE)); + assert_eq!(Ordering::Greater, (-min_subnorm()).total_cmp(&-max_subnorm())); + assert_eq!(Ordering::Greater, (-0.0_f64).total_cmp(&-min_subnorm())); + assert_eq!(Ordering::Greater, 0.0_f64.total_cmp(&-0.0)); + assert_eq!(Ordering::Greater, min_subnorm().total_cmp(&0.0)); + assert_eq!(Ordering::Greater, max_subnorm().total_cmp(&min_subnorm())); + assert_eq!(Ordering::Greater, f64::MIN_POSITIVE.total_cmp(&max_subnorm())); + assert_eq!(Ordering::Greater, 0.5_f64.total_cmp(&f64::MIN_POSITIVE)); + assert_eq!(Ordering::Greater, 1.0_f64.total_cmp(&0.5)); + assert_eq!(Ordering::Greater, 1.5_f64.total_cmp(&1.0)); + assert_eq!(Ordering::Greater, 2.5_f64.total_cmp(&1.5)); + assert_eq!(Ordering::Greater, f64::MAX.total_cmp(&2.5)); + assert_eq!(Ordering::Greater, f64::INFINITY.total_cmp(&f64::MAX)); + assert_eq!(Ordering::Greater, s_nan().total_cmp(&f64::INFINITY)); + assert_eq!(Ordering::Greater, q_nan().total_cmp(&s_nan())); + + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-s_nan())); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::INFINITY)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::MAX)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-2.5)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-1.5)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-1.0)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-0.5)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::MIN_POSITIVE)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-max_subnorm())); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-min_subnorm())); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-0.0)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&0.0)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&min_subnorm())); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&max_subnorm())); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::MIN_POSITIVE)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&0.5)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&1.0)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&1.5)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&2.5)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::MAX)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::INFINITY)); + assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&s_nan())); + + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::INFINITY)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::MAX)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-2.5)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-1.5)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-1.0)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-0.5)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::MIN_POSITIVE)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-max_subnorm())); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-min_subnorm())); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-0.0)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&0.0)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&min_subnorm())); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&max_subnorm())); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::MIN_POSITIVE)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&0.5)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&1.0)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&1.5)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&2.5)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::MAX)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::INFINITY)); + assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&s_nan())); + } +} |