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+//! 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()
+ }
+}