961 lines
29 KiB
Rust
961 lines
29 KiB
Rust
//! Constants for the `f32` single-precision floating point type.
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//!
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//! *[See also the `f32` primitive type](primitive@f32).*
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//!
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//! Mathematically significant numbers are provided in the `consts` sub-module.
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//!
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//! For the constants defined directly in this module
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//! (as distinct from those defined in the `consts` sub-module),
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//! new code should instead use the associated constants
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//! defined directly on the `f32` type.
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#![stable(feature = "rust1", since = "1.0.0")]
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#![allow(missing_docs)]
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#[cfg(test)]
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mod tests;
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#[cfg(not(test))]
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use crate::intrinsics;
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#[cfg(not(test))]
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use crate::sys::cmath;
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#[stable(feature = "rust1", since = "1.0.0")]
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#[allow(deprecated, deprecated_in_future)]
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pub use core::f32::{
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consts, DIGITS, EPSILON, INFINITY, MANTISSA_DIGITS, MAX, MAX_10_EXP, MAX_EXP, MIN, MIN_10_EXP,
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MIN_EXP, MIN_POSITIVE, NAN, NEG_INFINITY, RADIX,
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};
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#[cfg(not(test))]
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impl f32 {
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/// Returns the largest integer less than or equal to `self`.
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///
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/// # Examples
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///
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/// ```
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/// let f = 3.7_f32;
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/// let g = 3.0_f32;
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/// let h = -3.7_f32;
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///
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/// assert_eq!(f.floor(), 3.0);
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/// assert_eq!(g.floor(), 3.0);
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/// assert_eq!(h.floor(), -4.0);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn floor(self) -> f32 {
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unsafe { intrinsics::floorf32(self) }
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}
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/// Returns the smallest integer greater than or equal to `self`.
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///
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/// # Examples
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///
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/// ```
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/// let f = 3.01_f32;
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/// let g = 4.0_f32;
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///
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/// assert_eq!(f.ceil(), 4.0);
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/// assert_eq!(g.ceil(), 4.0);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn ceil(self) -> f32 {
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unsafe { intrinsics::ceilf32(self) }
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}
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/// Returns the nearest integer to `self`. If a value is half-way between two
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/// integers, round away from `0.0`.
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///
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/// # Examples
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///
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/// ```
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/// let f = 3.3_f32;
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/// let g = -3.3_f32;
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/// let h = -3.7_f32;
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/// let i = 3.5_f32;
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/// let j = 4.5_f32;
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///
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/// assert_eq!(f.round(), 3.0);
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/// assert_eq!(g.round(), -3.0);
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/// assert_eq!(h.round(), -4.0);
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/// assert_eq!(i.round(), 4.0);
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/// assert_eq!(j.round(), 5.0);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn round(self) -> f32 {
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unsafe { intrinsics::roundf32(self) }
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}
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/// Returns the nearest integer to a number. Rounds half-way cases to the number
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/// with an even least significant digit.
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///
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/// # Examples
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///
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/// ```
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/// #![feature(round_ties_even)]
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///
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/// let f = 3.3_f32;
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/// let g = -3.3_f32;
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/// let h = 3.5_f32;
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/// let i = 4.5_f32;
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///
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/// assert_eq!(f.round_ties_even(), 3.0);
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/// assert_eq!(g.round_ties_even(), -3.0);
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/// assert_eq!(h.round_ties_even(), 4.0);
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/// assert_eq!(i.round_ties_even(), 4.0);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[unstable(feature = "round_ties_even", issue = "96710")]
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#[inline]
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pub fn round_ties_even(self) -> f32 {
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unsafe { intrinsics::rintf32(self) }
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}
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/// Returns the integer part of `self`.
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/// This means that non-integer numbers are always truncated towards zero.
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///
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/// # Examples
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///
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/// ```
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/// let f = 3.7_f32;
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/// let g = 3.0_f32;
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/// let h = -3.7_f32;
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///
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/// assert_eq!(f.trunc(), 3.0);
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/// assert_eq!(g.trunc(), 3.0);
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/// assert_eq!(h.trunc(), -3.0);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn trunc(self) -> f32 {
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unsafe { intrinsics::truncf32(self) }
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}
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/// Returns the fractional part of `self`.
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///
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/// # Examples
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///
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/// ```
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/// let x = 3.6_f32;
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/// let y = -3.6_f32;
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/// let abs_difference_x = (x.fract() - 0.6).abs();
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/// let abs_difference_y = (y.fract() - (-0.6)).abs();
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///
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/// assert!(abs_difference_x <= f32::EPSILON);
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/// assert!(abs_difference_y <= f32::EPSILON);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn fract(self) -> f32 {
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self - self.trunc()
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}
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/// Computes the absolute value of `self`.
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///
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/// # Examples
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///
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/// ```
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/// let x = 3.5_f32;
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/// let y = -3.5_f32;
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///
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/// let abs_difference_x = (x.abs() - x).abs();
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/// let abs_difference_y = (y.abs() - (-y)).abs();
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///
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/// assert!(abs_difference_x <= f32::EPSILON);
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/// assert!(abs_difference_y <= f32::EPSILON);
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///
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/// assert!(f32::NAN.abs().is_nan());
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn abs(self) -> f32 {
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unsafe { intrinsics::fabsf32(self) }
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}
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/// Returns a number that represents the sign of `self`.
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///
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/// - `1.0` if the number is positive, `+0.0` or `INFINITY`
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/// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
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/// - NaN if the number is NaN
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///
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/// # Examples
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///
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/// ```
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/// let f = 3.5_f32;
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///
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/// assert_eq!(f.signum(), 1.0);
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/// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
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///
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/// assert!(f32::NAN.signum().is_nan());
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn signum(self) -> f32 {
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if self.is_nan() { Self::NAN } else { 1.0_f32.copysign(self) }
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}
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/// Returns a number composed of the magnitude of `self` and the sign of
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/// `sign`.
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///
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/// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
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/// equal to `-self`. If `self` is a NaN, then a NaN with the sign bit of
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/// `sign` is returned. Note, however, that conserving the sign bit on NaN
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/// across arithmetical operations is not generally guaranteed.
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/// See [explanation of NaN as a special value](primitive@f32) for more info.
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///
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/// # Examples
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///
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/// ```
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/// let f = 3.5_f32;
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///
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/// assert_eq!(f.copysign(0.42), 3.5_f32);
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/// assert_eq!(f.copysign(-0.42), -3.5_f32);
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/// assert_eq!((-f).copysign(0.42), 3.5_f32);
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/// assert_eq!((-f).copysign(-0.42), -3.5_f32);
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///
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/// assert!(f32::NAN.copysign(1.0).is_nan());
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[inline]
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#[stable(feature = "copysign", since = "1.35.0")]
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pub fn copysign(self, sign: f32) -> f32 {
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unsafe { intrinsics::copysignf32(self, sign) }
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}
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/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
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/// error, yielding a more accurate result than an unfused multiply-add.
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///
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/// Using `mul_add` *may* be more performant than an unfused multiply-add if
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/// the target architecture has a dedicated `fma` CPU instruction. However,
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/// this is not always true, and will be heavily dependant on designing
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/// algorithms with specific target hardware in mind.
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///
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/// # Examples
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///
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/// ```
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/// let m = 10.0_f32;
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/// let x = 4.0_f32;
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/// let b = 60.0_f32;
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///
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/// // 100.0
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/// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn mul_add(self, a: f32, b: f32) -> f32 {
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unsafe { intrinsics::fmaf32(self, a, b) }
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}
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/// Calculates Euclidean division, the matching method for `rem_euclid`.
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///
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/// This computes the integer `n` such that
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/// `self = n * rhs + self.rem_euclid(rhs)`.
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/// In other words, the result is `self / rhs` rounded to the integer `n`
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/// such that `self >= n * rhs`.
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///
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/// # Examples
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///
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/// ```
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/// let a: f32 = 7.0;
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/// let b = 4.0;
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/// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
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/// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
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/// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
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/// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[inline]
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#[stable(feature = "euclidean_division", since = "1.38.0")]
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pub fn div_euclid(self, rhs: f32) -> f32 {
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let q = (self / rhs).trunc();
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if self % rhs < 0.0 {
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return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
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}
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q
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}
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/// Calculates the least nonnegative remainder of `self (mod rhs)`.
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///
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/// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
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/// most cases. However, due to a floating point round-off error it can
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/// result in `r == rhs.abs()`, violating the mathematical definition, if
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/// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
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/// This result is not an element of the function's codomain, but it is the
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/// closest floating point number in the real numbers and thus fulfills the
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/// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
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/// approximately.
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///
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/// # Examples
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///
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/// ```
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/// let a: f32 = 7.0;
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/// let b = 4.0;
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/// assert_eq!(a.rem_euclid(b), 3.0);
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/// assert_eq!((-a).rem_euclid(b), 1.0);
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/// assert_eq!(a.rem_euclid(-b), 3.0);
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/// assert_eq!((-a).rem_euclid(-b), 1.0);
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/// // limitation due to round-off error
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/// assert!((-f32::EPSILON).rem_euclid(3.0) != 0.0);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[inline]
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#[stable(feature = "euclidean_division", since = "1.38.0")]
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pub fn rem_euclid(self, rhs: f32) -> f32 {
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let r = self % rhs;
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if r < 0.0 { r + rhs.abs() } else { r }
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}
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/// Raises a number to an integer power.
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///
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/// Using this function is generally faster than using `powf`.
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/// It might have a different sequence of rounding operations than `powf`,
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/// so the results are not guaranteed to agree.
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///
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/// # Examples
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///
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/// ```
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/// let x = 2.0_f32;
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/// let abs_difference = (x.powi(2) - (x * x)).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn powi(self, n: i32) -> f32 {
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unsafe { intrinsics::powif32(self, n) }
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}
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/// Raises a number to a floating point power.
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///
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/// # Examples
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///
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/// ```
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/// let x = 2.0_f32;
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/// let abs_difference = (x.powf(2.0) - (x * x)).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn powf(self, n: f32) -> f32 {
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unsafe { intrinsics::powf32(self, n) }
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}
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/// Returns the square root of a number.
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///
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/// Returns NaN if `self` is a negative number other than `-0.0`.
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///
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/// # Examples
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///
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/// ```
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/// let positive = 4.0_f32;
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/// let negative = -4.0_f32;
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/// let negative_zero = -0.0_f32;
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///
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/// let abs_difference = (positive.sqrt() - 2.0).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// assert!(negative.sqrt().is_nan());
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/// assert!(negative_zero.sqrt() == negative_zero);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn sqrt(self) -> f32 {
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unsafe { intrinsics::sqrtf32(self) }
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}
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/// Returns `e^(self)`, (the exponential function).
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///
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/// # Examples
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///
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/// ```
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/// let one = 1.0f32;
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/// // e^1
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/// let e = one.exp();
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///
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/// // ln(e) - 1 == 0
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/// let abs_difference = (e.ln() - 1.0).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[rustc_allow_incoherent_impl]
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|
#[must_use = "method returns a new number and does not mutate the original value"]
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|
#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn exp(self) -> f32 {
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unsafe { intrinsics::expf32(self) }
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}
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/// Returns `2^(self)`.
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///
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/// # Examples
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|
///
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|
/// ```
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/// let f = 2.0f32;
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///
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/// // 2^2 - 4 == 0
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/// let abs_difference = (f.exp2() - 4.0).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn exp2(self) -> f32 {
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unsafe { intrinsics::exp2f32(self) }
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}
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/// Returns the natural logarithm of the number.
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///
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/// # Examples
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///
|
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/// ```
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/// let one = 1.0f32;
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/// // e^1
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/// let e = one.exp();
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///
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/// // ln(e) - 1 == 0
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/// let abs_difference = (e.ln() - 1.0).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[rustc_allow_incoherent_impl]
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#[must_use = "method returns a new number and does not mutate the original value"]
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
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#[inline]
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pub fn ln(self) -> f32 {
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unsafe { intrinsics::logf32(self) }
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}
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|
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/// Returns the logarithm of the number with respect to an arbitrary base.
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///
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/// The result might not be correctly rounded owing to implementation details;
|
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/// `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 {
|
|
crate::sys::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) }
|
|
}
|
|
|
|
/// Compute the distance between the origin and a point (`x`, `y`) on the
|
|
/// Euclidean plane. Equivalently, compute the length of the hypotenuse of a
|
|
/// right-angle triangle with other sides having length `x.abs()` and
|
|
/// `y.abs()`.
|
|
///
|
|
/// # 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 {
|
|
let ax = self.abs();
|
|
let ix = 1.0 / ax;
|
|
(ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().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 - 1.0).sqrt() * (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()
|
|
}
|
|
}
|