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Diffstat (limited to 'library/std/src/f32.rs')
| -rw-r--r-- | library/std/src/f32.rs | 923 |
1 files changed, 923 insertions, 0 deletions
diff --git a/library/std/src/f32.rs b/library/std/src/f32.rs new file mode 100644 index 000000000..933b52b4d --- /dev/null +++ b/library/std/src/f32.rs @@ -0,0 +1,923 @@ +//! Constants specific to the `f32` single-precision floating point type. +//! +//! *[See also the `f32` primitive type](primitive@f32).* +//! +//! Mathematically significant numbers are provided in the `consts` sub-module. +//! +//! For the constants defined directly in this module +//! (as distinct from those defined in the `consts` sub-module), +//! new code should instead use the associated constants +//! defined directly on the `f32` type. + +#![stable(feature = "rust1", since = "1.0.0")] +#![allow(missing_docs)] + +#[cfg(test)] +mod tests; + +#[cfg(not(test))] +use crate::intrinsics; +#[cfg(not(test))] +use crate::sys::cmath; + +#[stable(feature = "rust1", since = "1.0.0")] +#[allow(deprecated, deprecated_in_future)] +pub use core::f32::{ + consts, DIGITS, EPSILON, INFINITY, MANTISSA_DIGITS, MAX, MAX_10_EXP, MAX_EXP, MIN, MIN_10_EXP, + MIN_EXP, MIN_POSITIVE, NAN, NEG_INFINITY, RADIX, +}; + +#[cfg(not(test))] +impl f32 { + /// Returns the largest integer less than or equal to `self`. + /// + /// # Examples + /// + /// ``` + /// let f = 3.7_f32; + /// let g = 3.0_f32; + /// let h = -3.7_f32; + /// + /// assert_eq!(f.floor(), 3.0); + /// assert_eq!(g.floor(), 3.0); + /// assert_eq!(h.floor(), -4.0); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::floorf32(self) } + } + + /// Returns the smallest integer greater than or equal to `self`. + /// + /// # Examples + /// + /// ``` + /// let f = 3.01_f32; + /// let g = 4.0_f32; + /// + /// assert_eq!(f.ceil(), 4.0); + /// assert_eq!(g.ceil(), 4.0); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::ceilf32(self) } + } + + /// Returns the nearest integer to `self`. Round half-way cases away from + /// `0.0`. + /// + /// # Examples + /// + /// ``` + /// let f = 3.3_f32; + /// let g = -3.3_f32; + /// + /// assert_eq!(f.round(), 3.0); + /// assert_eq!(g.round(), -3.0); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::roundf32(self) } + } + + /// Returns the integer part of `self`. + /// This means that non-integer numbers are always truncated towards zero. + /// + /// # Examples + /// + /// ``` + /// let f = 3.7_f32; + /// let g = 3.0_f32; + /// let h = -3.7_f32; + /// + /// assert_eq!(f.trunc(), 3.0); + /// assert_eq!(g.trunc(), 3.0); + /// assert_eq!(h.trunc(), -3.0); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::truncf32(self) } + } + + /// Returns the fractional part of `self`. + /// + /// # Examples + /// + /// ``` + /// let x = 3.6_f32; + /// let y = -3.6_f32; + /// let abs_difference_x = (x.fract() - 0.6).abs(); + /// let abs_difference_y = (y.fract() - (-0.6)).abs(); + /// + /// assert!(abs_difference_x <= f32::EPSILON); + /// assert!(abs_difference_y <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + self - self.trunc() + } + + /// Computes the absolute value of `self`. + /// + /// # Examples + /// + /// ``` + /// let x = 3.5_f32; + /// let y = -3.5_f32; + /// + /// let abs_difference_x = (x.abs() - x).abs(); + /// let abs_difference_y = (y.abs() - (-y)).abs(); + /// + /// assert!(abs_difference_x <= f32::EPSILON); + /// assert!(abs_difference_y <= f32::EPSILON); + /// + /// assert!(f32::NAN.abs().is_nan()); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::fabsf32(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_f32; + /// + /// assert_eq!(f.signum(), 1.0); + /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0); + /// + /// assert!(f32::NAN.signum().is_nan()); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + if self.is_nan() { Self::NAN } else { 1.0_f32.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 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. + /// + /// # Examples + /// + /// ``` + /// let f = 3.5_f32; + /// + /// assert_eq!(f.copysign(0.42), 3.5_f32); + /// assert_eq!(f.copysign(-0.42), -3.5_f32); + /// assert_eq!((-f).copysign(0.42), 3.5_f32); + /// assert_eq!((-f).copysign(-0.42), -3.5_f32); + /// + /// assert!(f32::NAN.copysign(1.0).is_nan()); + /// ``` + #[rustc_allow_incoherent_impl] + #[must_use = "method returns a new number and does not mutate the original value"] + #[inline] + #[stable(feature = "copysign", since = "1.35.0")] + pub fn copysign(self, sign: f32) -> f32 { + unsafe { intrinsics::copysignf32(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` *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. + /// + /// # Examples + /// + /// ``` + /// let m = 10.0_f32; + /// let x = 4.0_f32; + /// let b = 60.0_f32; + /// + /// // 100.0 + /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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: f32, b: f32) -> f32 { + unsafe { intrinsics::fmaf32(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: f32 = 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 + /// ``` + #[rustc_allow_incoherent_impl] + #[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: f32) -> f32 { + 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: f32 = 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!((-f32::EPSILON).rem_euclid(3.0) != 0.0); + /// ``` + #[rustc_allow_incoherent_impl] + #[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: f32) -> f32 { + 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`. + /// It might have a different sequence of rounding operations than `powf`, + /// so the results are not guaranteed to agree. + /// + /// # Examples + /// + /// ``` + /// let x = 2.0_f32; + /// let abs_difference = (x.powi(2) - (x * x)).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::powif32(self, n) } + } + + /// Raises a number to a floating point power. + /// + /// # Examples + /// + /// ``` + /// let x = 2.0_f32; + /// let abs_difference = (x.powf(2.0) - (x * x)).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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: f32) -> f32 { + unsafe { intrinsics::powf32(self, n) } + } + + /// Returns the square root of a number. + /// + /// Returns NaN if `self` is a negative number other than `-0.0`. + /// + /// # Examples + /// + /// ``` + /// let positive = 4.0_f32; + /// let negative = -4.0_f32; + /// let negative_zero = -0.0_f32; + /// + /// let abs_difference = (positive.sqrt() - 2.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// assert!(negative.sqrt().is_nan()); + /// assert!(negative_zero.sqrt() == negative_zero); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::sqrtf32(self) } + } + + /// Returns `e^(self)`, (the exponential function). + /// + /// # Examples + /// + /// ``` + /// let one = 1.0f32; + /// // e^1 + /// let e = one.exp(); + /// + /// // ln(e) - 1 == 0 + /// let abs_difference = (e.ln() - 1.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::expf32(self) } + } + + /// Returns `2^(self)`. + /// + /// # Examples + /// + /// ``` + /// let f = 2.0f32; + /// + /// // 2^2 - 4 == 0 + /// let abs_difference = (f.exp2() - 4.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::exp2f32(self) } + } + + /// Returns the natural logarithm of the number. + /// + /// # Examples + /// + /// ``` + /// let one = 1.0f32; + /// // e^1 + /// let e = one.exp(); + /// + /// // ln(e) - 1 == 0 + /// let abs_difference = (e.ln() - 1.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::logf32(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. + /// + /// # Examples + /// + /// ``` + /// let five = 5.0f32; + /// + /// // log5(5) - 1 == 0 + /// let abs_difference = (five.log(5.0) - 1.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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: f32) -> f32 { + self.ln() / base.ln() + } + + /// Returns the base 2 logarithm of the number. + /// + /// # Examples + /// + /// ``` + /// let two = 2.0f32; + /// + /// // log2(2) - 1 == 0 + /// let abs_difference = (two.log2() - 1.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + #[cfg(target_os = "android")] + return crate::sys::android::log2f32(self); + #[cfg(not(target_os = "android"))] + return unsafe { intrinsics::log2f32(self) }; + } + + /// Returns the base 10 logarithm of the number. + /// + /// # Examples + /// + /// ``` + /// let ten = 10.0f32; + /// + /// // log10(10) - 1 == 0 + /// let abs_difference = (ten.log10() - 1.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::log10f32(self) } + } + + /// The positive difference of two numbers. + /// + /// * If `self <= other`: `0:0` + /// * Else: `self - other` + /// + /// # Examples + /// + /// ``` + /// let x = 3.0f32; + /// let y = -3.0f32; + /// + /// 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 <= f32::EPSILON); + /// assert!(abs_difference_y <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[must_use = "method returns a new number and does not mutate the original value"] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + #[deprecated( + since = "1.10.0", + note = "you probably meant `(self - other).abs()`: \ + this operation is `(self - other).max(0.0)` \ + except that `abs_sub` also propagates NaNs (also \ + known as `fdimf` in C). If you truly need the positive \ + difference, consider using that expression or the C function \ + `fdimf`, depending on how you wish to handle NaN (please consider \ + filing an issue describing your use-case too)." + )] + pub fn abs_sub(self, other: f32) -> f32 { + unsafe { cmath::fdimf(self, other) } + } + + /// Returns the cube root of a number. + /// + /// # Examples + /// + /// ``` + /// let x = 8.0f32; + /// + /// // x^(1/3) - 2 == 0 + /// let abs_difference = (x.cbrt() - 2.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { cmath::cbrtf(self) } + } + + /// Calculates the length of the hypotenuse of a right-angle triangle given + /// legs of length `x` and `y`. + /// + /// # Examples + /// + /// ``` + /// let x = 2.0f32; + /// let y = 3.0f32; + /// + /// // sqrt(x^2 + y^2) + /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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: f32) -> f32 { + unsafe { cmath::hypotf(self, other) } + } + + /// Computes the sine of a number (in radians). + /// + /// # Examples + /// + /// ``` + /// let x = std::f32::consts::FRAC_PI_2; + /// + /// let abs_difference = (x.sin() - 1.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::sinf32(self) } + } + + /// Computes the cosine of a number (in radians). + /// + /// # Examples + /// + /// ``` + /// let x = 2.0 * std::f32::consts::PI; + /// + /// let abs_difference = (x.cos() - 1.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { intrinsics::cosf32(self) } + } + + /// Computes the tangent of a number (in radians). + /// + /// # Examples + /// + /// ``` + /// let x = std::f32::consts::FRAC_PI_4; + /// let abs_difference = (x.tan() - 1.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { cmath::tanf(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::f32::consts::FRAC_PI_2; + /// + /// // asin(sin(pi/2)) + /// let abs_difference = (f.sin().asin() - std::f32::consts::FRAC_PI_2).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { cmath::asinf(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::f32::consts::FRAC_PI_4; + /// + /// // acos(cos(pi/4)) + /// let abs_difference = (f.cos().acos() - std::f32::consts::FRAC_PI_4).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { cmath::acosf(self) } + } + + /// Computes the arctangent of a number. Return value is in radians in the + /// range [-pi/2, pi/2]; + /// + /// # Examples + /// + /// ``` + /// let f = 1.0f32; + /// + /// // atan(tan(1)) + /// let abs_difference = (f.tan().atan() - 1.0).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { cmath::atanf(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 = 3.0f32; + /// let y1 = -3.0f32; + /// + /// // 3pi/4 radians (135 deg counter-clockwise) + /// let x2 = -3.0f32; + /// let y2 = 3.0f32; + /// + /// let abs_difference_1 = (y1.atan2(x1) - (-std::f32::consts::FRAC_PI_4)).abs(); + /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f32::consts::FRAC_PI_4)).abs(); + /// + /// assert!(abs_difference_1 <= f32::EPSILON); + /// assert!(abs_difference_2 <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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: f32) -> f32 { + unsafe { cmath::atan2f(self, other) } + } + + /// Simultaneously computes the sine and cosine of the number, `x`. Returns + /// `(sin(x), cos(x))`. + /// + /// # Examples + /// + /// ``` + /// let x = std::f32::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 <= f32::EPSILON); + /// assert!(abs_difference_1 <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[stable(feature = "rust1", since = "1.0.0")] + #[inline] + pub fn sin_cos(self) -> (f32, f32) { + (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 = 1e-8_f32; + /// + /// // for very small x, e^x is approximately 1 + x + x^2 / 2 + /// let approx = x + x * x / 2.0; + /// let abs_difference = (x.exp_m1() - approx).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { cmath::expm1f(self) } + } + + /// Returns `ln(1+n)` (natural logarithm) more accurately than if + /// the operations were performed separately. + /// + /// # Examples + /// + /// ``` + /// let x = 1e-8_f32; + /// + /// // for very small x, ln(1 + x) is approximately x - x^2 / 2 + /// let approx = x - x * x / 2.0; + /// let abs_difference = (x.ln_1p() - approx).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { cmath::log1pf(self) } + } + + /// Hyperbolic sine function. + /// + /// # Examples + /// + /// ``` + /// let e = std::f32::consts::E; + /// let x = 1.0f32; + /// + /// 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 <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { cmath::sinhf(self) } + } + + /// Hyperbolic cosine function. + /// + /// # Examples + /// + /// ``` + /// let e = std::f32::consts::E; + /// let x = 1.0f32; + /// 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 <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { cmath::coshf(self) } + } + + /// Hyperbolic tangent function. + /// + /// # Examples + /// + /// ``` + /// let e = std::f32::consts::E; + /// let x = 1.0f32; + /// + /// 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 <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + unsafe { cmath::tanhf(self) } + } + + /// Inverse hyperbolic sine function. + /// + /// # Examples + /// + /// ``` + /// let x = 1.0f32; + /// let f = x.sinh().asinh(); + /// + /// let abs_difference = (f - x).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + (self.abs() + ((self * self) + 1.0).sqrt()).ln().copysign(self) + } + + /// Inverse hyperbolic cosine function. + /// + /// # Examples + /// + /// ``` + /// let x = 1.0f32; + /// let f = x.cosh().acosh(); + /// + /// let abs_difference = (f - x).abs(); + /// + /// assert!(abs_difference <= f32::EPSILON); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + if self < 1.0 { Self::NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() } + } + + /// Inverse hyperbolic tangent function. + /// + /// # Examples + /// + /// ``` + /// let e = std::f32::consts::E; + /// let f = e.tanh().atanh(); + /// + /// let abs_difference = (f - e).abs(); + /// + /// assert!(abs_difference <= 1e-5); + /// ``` + #[rustc_allow_incoherent_impl] + #[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) -> f32 { + 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p() + } +} |