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rust / rust-lang / rust / refs/heads/try / . / library / std / src / num / f16.rs
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//! Constants for the `f16` half-precision floating point type.
//!
//! *[See also the `f16` primitive type](primitive@f16).*
//!
//! Mathematically significant numbers are provided in the `consts` sub-module.
#![unstable(feature = "f16", issue = "116909")]
#![doc(test(attr(feature(cfg_target_has_reliable_f16_f128), expect(internal_features))))]
#[unstable(feature = "f16", issue = "116909")]
pub use core::f16::consts;
#[cfg(not(test))]
use crate::intrinsics;
#[cfg(not(test))]
use crate::sys::cmath;
#[cfg(not(test))]
impl f16 {
/// Raises a number to a floating point power.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = 2.0_f16;
/// let abs_difference = (x.powf(2.0) - (x * x)).abs();
/// assert!(abs_difference <= f16::EPSILON);
///
/// assert_eq!(f16::powf(1.0, f16::NAN), 1.0);
/// assert_eq!(f16::powf(f16::NAN, 0.0), 1.0);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn powf(self, n: f16) -> f16 {
unsafe { intrinsics::powf16(self, n) }
}
/// Returns `e^(self)`, (the exponential function).
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let one = 1.0f16;
/// // e^1
/// let e = one.exp();
///
/// // ln(e) - 1 == 0
/// let abs_difference = (e.ln() - 1.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn exp(self) -> f16 {
unsafe { intrinsics::expf16(self) }
}
/// Returns `2^(self)`.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let f = 2.0f16;
///
/// // 2^2 - 4 == 0
/// let abs_difference = (f.exp2() - 4.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn exp2(self) -> f16 {
unsafe { intrinsics::exp2f16(self) }
}
/// Returns the natural logarithm of the number.
///
/// This returns NaN when the number is negative, and negative infinity when number is zero.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let one = 1.0f16;
/// // e^1
/// let e = one.exp();
///
/// // ln(e) - 1 == 0
/// let abs_difference = (e.ln() - 1.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
///
/// Non-positive values:
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// assert_eq!(0_f16.ln(), f16::NEG_INFINITY);
/// assert!((-42_f16).ln().is_nan());
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn ln(self) -> f16 {
unsafe { intrinsics::logf16(self) }
}
/// Returns the logarithm of the number with respect to an arbitrary base.
///
/// This returns NaN when the number is negative, and negative infinity when number is zero.
///
/// 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.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let five = 5.0f16;
///
/// // log5(5) - 1 == 0
/// let abs_difference = (five.log(5.0) - 1.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
///
/// Non-positive values:
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// assert_eq!(0_f16.log(10.0), f16::NEG_INFINITY);
/// assert!((-42_f16).log(10.0).is_nan());
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn log(self, base: f16) -> f16 {
self.ln() / base.ln()
}
/// Returns the base 2 logarithm of the number.
///
/// This returns NaN when the number is negative, and negative infinity when number is zero.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let two = 2.0f16;
///
/// // log2(2) - 1 == 0
/// let abs_difference = (two.log2() - 1.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
///
/// Non-positive values:
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// assert_eq!(0_f16.log2(), f16::NEG_INFINITY);
/// assert!((-42_f16).log2().is_nan());
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn log2(self) -> f16 {
unsafe { intrinsics::log2f16(self) }
}
/// Returns the base 10 logarithm of the number.
///
/// This returns NaN when the number is negative, and negative infinity when number is zero.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let ten = 10.0f16;
///
/// // log10(10) - 1 == 0
/// let abs_difference = (ten.log10() - 1.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
///
/// Non-positive values:
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// assert_eq!(0_f16.log10(), f16::NEG_INFINITY);
/// assert!((-42_f16).log10().is_nan());
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn log10(self) -> f16 {
unsafe { intrinsics::log10f16(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()`.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `hypotf` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = 2.0f16;
/// let y = 3.0f16;
///
/// // sqrt(x^2 + y^2)
/// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn hypot(self, other: f16) -> f16 {
cmath::hypotf(self as f32, other as f32) as f16
}
/// Computes the sine of a number (in radians).
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = std::f16::consts::FRAC_PI_2;
///
/// let abs_difference = (x.sin() - 1.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn sin(self) -> f16 {
unsafe { intrinsics::sinf16(self) }
}
/// Computes the cosine of a number (in radians).
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = 2.0 * std::f16::consts::PI;
///
/// let abs_difference = (x.cos() - 1.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn cos(self) -> f16 {
unsafe { intrinsics::cosf16(self) }
}
/// Computes the tangent of a number (in radians).
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `tanf` from libc on Unix and
/// Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = std::f16::consts::FRAC_PI_4;
/// let abs_difference = (x.tan() - 1.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn tan(self) -> f16 {
cmath::tanf(self as f32) as f16
}
/// 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].
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `asinf` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let f = std::f16::consts::FRAC_PI_2;
///
/// // asin(sin(pi/2))
/// let abs_difference = (f.sin().asin() - std::f16::consts::FRAC_PI_2).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[doc(alias = "arcsin")]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn asin(self) -> f16 {
cmath::asinf(self as f32) as f16
}
/// 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].
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `acosf` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let f = std::f16::consts::FRAC_PI_4;
///
/// // acos(cos(pi/4))
/// let abs_difference = (f.cos().acos() - std::f16::consts::FRAC_PI_4).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[doc(alias = "arccos")]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn acos(self) -> f16 {
cmath::acosf(self as f32) as f16
}
/// Computes the arctangent of a number. Return value is in radians in the
/// range [-pi/2, pi/2];
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `atanf` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let f = 1.0f16;
///
/// // atan(tan(1))
/// let abs_difference = (f.tan().atan() - 1.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[doc(alias = "arctan")]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn atan(self) -> f16 {
cmath::atanf(self as f32) as f16
}
/// 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)`
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `atan2f` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// // Positive angles measured counter-clockwise
/// // from positive x axis
/// // -pi/4 radians (45 deg clockwise)
/// let x1 = 3.0f16;
/// let y1 = -3.0f16;
///
/// // 3pi/4 radians (135 deg counter-clockwise)
/// let x2 = -3.0f16;
/// let y2 = 3.0f16;
///
/// let abs_difference_1 = (y1.atan2(x1) - (-std::f16::consts::FRAC_PI_4)).abs();
/// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f16::consts::FRAC_PI_4)).abs();
///
/// assert!(abs_difference_1 <= f16::EPSILON);
/// assert!(abs_difference_2 <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn atan2(self, other: f16) -> f16 {
cmath::atan2f(self as f32, other as f32) as f16
}
/// Simultaneously computes the sine and cosine of the number, `x`. Returns
/// `(sin(x), cos(x))`.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `(f16::sin(x),
/// f16::cos(x))`. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = std::f16::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 <= f16::EPSILON);
/// assert!(abs_difference_1 <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[doc(alias = "sincos")]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
pub fn sin_cos(self) -> (f16, f16) {
(self.sin(), self.cos())
}
/// Returns `e^(self) - 1` in a way that is accurate even if the
/// number is close to zero.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `expm1f` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = 1e-4_f16;
///
/// // 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-4);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn exp_m1(self) -> f16 {
cmath::expm1f(self as f32) as f16
}
/// Returns `ln(1+n)` (natural logarithm) more accurately than if
/// the operations were performed separately.
///
/// This returns NaN when `n < -1.0`, and negative infinity when `n == -1.0`.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `log1pf` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = 1e-4_f16;
///
/// // 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-4);
/// # }
/// ```
///
/// Out-of-range values:
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// assert_eq!((-1.0_f16).ln_1p(), f16::NEG_INFINITY);
/// assert!((-2.0_f16).ln_1p().is_nan());
/// # }
/// ```
#[inline]
#[doc(alias = "log1p")]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn ln_1p(self) -> f16 {
cmath::log1pf(self as f32) as f16
}
/// Hyperbolic sine function.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `sinhf` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let e = std::f16::consts::E;
/// let x = 1.0f16;
///
/// 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 <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn sinh(self) -> f16 {
cmath::sinhf(self as f32) as f16
}
/// Hyperbolic cosine function.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `coshf` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let e = std::f16::consts::E;
/// let x = 1.0f16;
/// 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 <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn cosh(self) -> f16 {
cmath::coshf(self as f32) as f16
}
/// Hyperbolic tangent function.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `tanhf` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let e = std::f16::consts::E;
/// let x = 1.0f16;
///
/// 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 <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn tanh(self) -> f16 {
cmath::tanhf(self as f32) as f16
}
/// Inverse hyperbolic sine function.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = 1.0f16;
/// let f = x.sinh().asinh();
///
/// let abs_difference = (f - x).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[doc(alias = "arcsinh")]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn asinh(self) -> f16 {
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.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = 1.0f16;
/// let f = x.cosh().acosh();
///
/// let abs_difference = (f - x).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[doc(alias = "arccosh")]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn acosh(self) -> f16 {
if self < 1.0 {
Self::NAN
} else {
(self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
}
}
/// Inverse hyperbolic tangent function.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let e = std::f16::consts::E;
/// let f = e.tanh().atanh();
///
/// let abs_difference = (f - e).abs();
///
/// assert!(abs_difference <= 0.01);
/// # }
/// ```
#[inline]
#[doc(alias = "arctanh")]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn atanh(self) -> f16 {
0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
}
/// Gamma function.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `tgammaf` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// #![feature(float_gamma)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = 5.0f16;
///
/// let abs_difference = (x.gamma() - 24.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
// #[unstable(feature = "float_gamma", issue = "99842")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn gamma(self) -> f16 {
cmath::tgammaf(self as f32) as f16
}
/// Natural logarithm of the absolute value of the gamma function
///
/// The integer part of the tuple indicates the sign of the gamma function.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `lgamma_r` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// #![feature(float_gamma)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = 2.0f16;
///
/// let abs_difference = (x.ln_gamma().0 - 0.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
// #[unstable(feature = "float_gamma", issue = "99842")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn ln_gamma(self) -> (f16, i32) {
let mut signgamp: i32 = 0;
let x = cmath::lgammaf_r(self as f32, &mut signgamp) as f16;
(x, signgamp)
}
/// Error function.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `erff` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// #![feature(float_erf)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
/// /// The error function relates what percent of a normal distribution lies
/// /// within `x` standard deviations (scaled by `1/sqrt(2)`).
/// fn within_standard_deviations(x: f16) -> f16 {
/// (x * std::f16::consts::FRAC_1_SQRT_2).erf() * 100.0
/// }
///
/// // 68% of a normal distribution is within one standard deviation
/// assert!((within_standard_deviations(1.0) - 68.269).abs() < 0.1);
/// // 95% of a normal distribution is within two standard deviations
/// assert!((within_standard_deviations(2.0) - 95.450).abs() < 0.1);
/// // 99.7% of a normal distribution is within three standard deviations
/// assert!((within_standard_deviations(3.0) - 99.730).abs() < 0.1);
/// # }
/// ```
#[rustc_allow_incoherent_impl]
#[must_use = "method returns a new number and does not mutate the original value"]
#[unstable(feature = "f16", issue = "116909")]
// #[unstable(feature = "float_erf", issue = "136321")]
#[inline]
pub fn erf(self) -> f16 {
cmath::erff(self as f32) as f16
}
/// Complementary error function.
///
/// # Unspecified precision
///
/// The precision of this function is non-deterministic. This means it varies by platform,
/// Rust version, and can even differ within the same execution from one invocation to the next.
///
/// This function currently corresponds to the `erfcf` from libc on Unix
/// and Windows. Note that this might change in the future.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// #![feature(float_erf)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
/// let x: f16 = 0.123;
///
/// let one = x.erf() + x.erfc();
/// let abs_difference = (one - 1.0).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[rustc_allow_incoherent_impl]
#[must_use = "method returns a new number and does not mutate the original value"]
#[unstable(feature = "f16", issue = "116909")]
// #[unstable(feature = "float_erf", issue = "136321")]
#[inline]
pub fn erfc(self) -> f16 {
cmath::erfcf(self as f32) as f16
}
}