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fuchsia / third_party / rust / eda6dc928323fcd0ac1b51cea1aa79ab17e8519d / . / library / core / src / num / f16.rs
blob: 23a8661c14b7ac8018dfa75065d6a4f86f0e90d9 [file] [log] [blame]
//! Constants for the `f16` half-precision floating point type.
//!
//! *[See also the `f16` primitive type][f16].*
//!
//! 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 `f16` type.
#![unstable(feature = "f16", issue = "116909")]
use crate::convert::FloatToInt;
use crate::num::FpCategory;
#[cfg(not(test))]
use crate::num::libm;
use crate::panic::const_assert;
use crate::{intrinsics, mem};
/// Basic mathematical constants.
#[unstable(feature = "f16", issue = "116909")]
pub mod consts {
// FIXME: replace with mathematical constants from cmath.
/// Archimedes' constant (π)
#[unstable(feature = "f16", issue = "116909")]
pub const PI: f16 = 3.14159265358979323846264338327950288_f16;
/// The full circle constant (τ)
///
/// Equal to 2π.
#[unstable(feature = "f16", issue = "116909")]
pub const TAU: f16 = 6.28318530717958647692528676655900577_f16;
/// The golden ratio (φ)
#[unstable(feature = "f16", issue = "116909")]
// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
pub const PHI: f16 = 1.618033988749894848204586834365638118_f16;
/// The Euler-Mascheroni constant (γ)
#[unstable(feature = "f16", issue = "116909")]
// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
pub const EGAMMA: f16 = 0.577215664901532860606512090082402431_f16;
/// π/2
#[unstable(feature = "f16", issue = "116909")]
pub const FRAC_PI_2: f16 = 1.57079632679489661923132169163975144_f16;
/// π/3
#[unstable(feature = "f16", issue = "116909")]
pub const FRAC_PI_3: f16 = 1.04719755119659774615421446109316763_f16;
/// π/4
#[unstable(feature = "f16", issue = "116909")]
pub const FRAC_PI_4: f16 = 0.785398163397448309615660845819875721_f16;
/// π/6
#[unstable(feature = "f16", issue = "116909")]
pub const FRAC_PI_6: f16 = 0.52359877559829887307710723054658381_f16;
/// π/8
#[unstable(feature = "f16", issue = "116909")]
pub const FRAC_PI_8: f16 = 0.39269908169872415480783042290993786_f16;
/// 1/π
#[unstable(feature = "f16", issue = "116909")]
pub const FRAC_1_PI: f16 = 0.318309886183790671537767526745028724_f16;
/// 1/sqrt(π)
#[unstable(feature = "f16", issue = "116909")]
// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
pub const FRAC_1_SQRT_PI: f16 = 0.564189583547756286948079451560772586_f16;
/// 1/sqrt(2π)
#[doc(alias = "FRAC_1_SQRT_TAU")]
#[unstable(feature = "f16", issue = "116909")]
// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
pub const FRAC_1_SQRT_2PI: f16 = 0.398942280401432677939946059934381868_f16;
/// 2/π
#[unstable(feature = "f16", issue = "116909")]
pub const FRAC_2_PI: f16 = 0.636619772367581343075535053490057448_f16;
/// 2/sqrt(π)
#[unstable(feature = "f16", issue = "116909")]
pub const FRAC_2_SQRT_PI: f16 = 1.12837916709551257389615890312154517_f16;
/// sqrt(2)
#[unstable(feature = "f16", issue = "116909")]
pub const SQRT_2: f16 = 1.41421356237309504880168872420969808_f16;
/// 1/sqrt(2)
#[unstable(feature = "f16", issue = "116909")]
pub const FRAC_1_SQRT_2: f16 = 0.707106781186547524400844362104849039_f16;
/// sqrt(3)
#[unstable(feature = "f16", issue = "116909")]
// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
pub const SQRT_3: f16 = 1.732050807568877293527446341505872367_f16;
/// 1/sqrt(3)
#[unstable(feature = "f16", issue = "116909")]
// Also, #[unstable(feature = "more_float_constants", issue = "103883")]
pub const FRAC_1_SQRT_3: f16 = 0.577350269189625764509148780501957456_f16;
/// Euler's number (e)
#[unstable(feature = "f16", issue = "116909")]
pub const E: f16 = 2.71828182845904523536028747135266250_f16;
/// log<sub>2</sub>(10)
#[unstable(feature = "f16", issue = "116909")]
pub const LOG2_10: f16 = 3.32192809488736234787031942948939018_f16;
/// log<sub>2</sub>(e)
#[unstable(feature = "f16", issue = "116909")]
pub const LOG2_E: f16 = 1.44269504088896340735992468100189214_f16;
/// log<sub>10</sub>(2)
#[unstable(feature = "f16", issue = "116909")]
pub const LOG10_2: f16 = 0.301029995663981195213738894724493027_f16;
/// log<sub>10</sub>(e)
#[unstable(feature = "f16", issue = "116909")]
pub const LOG10_E: f16 = 0.434294481903251827651128918916605082_f16;
/// ln(2)
#[unstable(feature = "f16", issue = "116909")]
pub const LN_2: f16 = 0.693147180559945309417232121458176568_f16;
/// ln(10)
#[unstable(feature = "f16", issue = "116909")]
pub const LN_10: f16 = 2.30258509299404568401799145468436421_f16;
}
impl f16 {
// FIXME(f16_f128): almost all methods in this `impl` are missing examples and a const
// implementation. Add these once we can run code on all platforms and have f16/f128 in CTFE.
/// The radix or base of the internal representation of `f16`.
#[unstable(feature = "f16", issue = "116909")]
pub const RADIX: u32 = 2;
/// Number of significant digits in base 2.
///
/// Note that the size of the mantissa in the bitwise representation is one
/// smaller than this since the leading 1 is not stored explicitly.
#[unstable(feature = "f16", issue = "116909")]
pub const MANTISSA_DIGITS: u32 = 11;
/// Approximate number of significant digits in base 10.
///
/// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
/// significant digits can be converted to `f16` and back without loss.
///
/// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
///
/// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
#[unstable(feature = "f16", issue = "116909")]
pub const DIGITS: u32 = 3;
/// [Machine epsilon] value for `f16`.
///
/// This is the difference between `1.0` and the next larger representable number.
///
/// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
///
/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
/// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
#[unstable(feature = "f16", issue = "116909")]
#[rustc_diagnostic_item = "f16_epsilon"]
pub const EPSILON: f16 = 9.7656e-4_f16;
/// Smallest finite `f16` value.
///
/// Equal to &minus;[`MAX`].
///
/// [`MAX`]: f16::MAX
#[unstable(feature = "f16", issue = "116909")]
pub const MIN: f16 = -6.5504e+4_f16;
/// Smallest positive normal `f16` value.
///
/// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
///
/// [`MIN_EXP`]: f16::MIN_EXP
#[unstable(feature = "f16", issue = "116909")]
pub const MIN_POSITIVE: f16 = 6.1035e-5_f16;
/// Largest finite `f16` value.
///
/// Equal to
/// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
///
/// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
/// [`MAX_EXP`]: f16::MAX_EXP
#[unstable(feature = "f16", issue = "116909")]
pub const MAX: f16 = 6.5504e+4_f16;
/// One greater than the minimum possible *normal* power of 2 exponent
/// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
///
/// This corresponds to the exact minimum possible *normal* power of 2 exponent
/// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
/// In other words, all normal numbers representable by this type are
/// greater than or equal to 0.5&nbsp;×&nbsp;2<sup><i>MIN_EXP</i></sup>.
#[unstable(feature = "f16", issue = "116909")]
pub const MIN_EXP: i32 = -13;
/// One greater than the maximum possible power of 2 exponent
/// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
///
/// This corresponds to the exact maximum possible power of 2 exponent
/// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
/// In other words, all numbers representable by this type are
/// strictly less than 2<sup><i>MAX_EXP</i></sup>.
#[unstable(feature = "f16", issue = "116909")]
pub const MAX_EXP: i32 = 16;
/// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
///
/// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
///
/// [`MIN_POSITIVE`]: f16::MIN_POSITIVE
#[unstable(feature = "f16", issue = "116909")]
pub const MIN_10_EXP: i32 = -4;
/// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
///
/// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
///
/// [`MAX`]: f16::MAX
#[unstable(feature = "f16", issue = "116909")]
pub const MAX_10_EXP: i32 = 4;
/// Not a Number (NaN).
///
/// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
/// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
/// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
/// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
/// info.
///
/// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
/// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
/// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
/// The concrete bit pattern may change across Rust versions and target platforms.
#[allow(clippy::eq_op)]
#[rustc_diagnostic_item = "f16_nan"]
#[unstable(feature = "f16", issue = "116909")]
pub const NAN: f16 = 0.0_f16 / 0.0_f16;
/// Infinity (∞).
#[unstable(feature = "f16", issue = "116909")]
pub const INFINITY: f16 = 1.0_f16 / 0.0_f16;
/// Negative infinity (−∞).
#[unstable(feature = "f16", issue = "116909")]
pub const NEG_INFINITY: f16 = -1.0_f16 / 0.0_f16;
/// Sign bit
pub(crate) const SIGN_MASK: u16 = 0x8000;
/// Exponent mask
pub(crate) const EXP_MASK: u16 = 0x7c00;
/// Mantissa mask
pub(crate) const MAN_MASK: u16 = 0x03ff;
/// Minimum representable positive value (min subnormal)
const TINY_BITS: u16 = 0x1;
/// Minimum representable negative value (min negative subnormal)
const NEG_TINY_BITS: u16 = Self::TINY_BITS | Self::SIGN_MASK;
/// Returns `true` if this value is NaN.
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let nan = f16::NAN;
/// let f = 7.0_f16;
///
/// assert!(nan.is_nan());
/// assert!(!f.is_nan());
/// # }
/// ```
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
#[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
pub const fn is_nan(self) -> bool {
self != self
}
/// Returns `true` if this value is positive infinity or negative infinity, and
/// `false` otherwise.
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let f = 7.0f16;
/// let inf = f16::INFINITY;
/// let neg_inf = f16::NEG_INFINITY;
/// let nan = f16::NAN;
///
/// assert!(!f.is_infinite());
/// assert!(!nan.is_infinite());
///
/// assert!(inf.is_infinite());
/// assert!(neg_inf.is_infinite());
/// # }
/// ```
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
pub const fn is_infinite(self) -> bool {
(self == f16::INFINITY) | (self == f16::NEG_INFINITY)
}
/// Returns `true` if this number is neither infinite nor NaN.
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let f = 7.0f16;
/// let inf: f16 = f16::INFINITY;
/// let neg_inf: f16 = f16::NEG_INFINITY;
/// let nan: f16 = f16::NAN;
///
/// assert!(f.is_finite());
///
/// assert!(!nan.is_finite());
/// assert!(!inf.is_finite());
/// assert!(!neg_inf.is_finite());
/// # }
/// ```
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
pub const fn is_finite(self) -> bool {
// There's no need to handle NaN separately: if self is NaN,
// the comparison is not true, exactly as desired.
self.abs() < Self::INFINITY
}
/// Returns `true` if the number is [subnormal].
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let min = f16::MIN_POSITIVE; // 6.1035e-5
/// let max = f16::MAX;
/// let lower_than_min = 1.0e-7_f16;
/// let zero = 0.0_f16;
///
/// assert!(!min.is_subnormal());
/// assert!(!max.is_subnormal());
///
/// assert!(!zero.is_subnormal());
/// assert!(!f16::NAN.is_subnormal());
/// assert!(!f16::INFINITY.is_subnormal());
/// // Values between `0` and `min` are Subnormal.
/// assert!(lower_than_min.is_subnormal());
/// # }
/// ```
/// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
pub const fn is_subnormal(self) -> bool {
matches!(self.classify(), FpCategory::Subnormal)
}
/// Returns `true` if the number is neither zero, infinite, [subnormal], or NaN.
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let min = f16::MIN_POSITIVE; // 6.1035e-5
/// let max = f16::MAX;
/// let lower_than_min = 1.0e-7_f16;
/// let zero = 0.0_f16;
///
/// assert!(min.is_normal());
/// assert!(max.is_normal());
///
/// assert!(!zero.is_normal());
/// assert!(!f16::NAN.is_normal());
/// assert!(!f16::INFINITY.is_normal());
/// // Values between `0` and `min` are Subnormal.
/// assert!(!lower_than_min.is_normal());
/// # }
/// ```
/// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
pub const fn is_normal(self) -> bool {
matches!(self.classify(), FpCategory::Normal)
}
/// Returns the floating point category of the number. If only one property
/// is going to be tested, it is generally faster to use the specific
/// predicate instead.
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// use std::num::FpCategory;
///
/// let num = 12.4_f16;
/// let inf = f16::INFINITY;
///
/// assert_eq!(num.classify(), FpCategory::Normal);
/// assert_eq!(inf.classify(), FpCategory::Infinite);
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
pub const fn classify(self) -> FpCategory {
let b = self.to_bits();
match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
(0, Self::EXP_MASK) => FpCategory::Infinite,
(_, Self::EXP_MASK) => FpCategory::Nan,
(0, 0) => FpCategory::Zero,
(_, 0) => FpCategory::Subnormal,
_ => FpCategory::Normal,
}
}
/// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
/// positive sign bit and positive infinity.
///
/// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
/// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
/// conserved over arithmetic operations, the result of `is_sign_positive` on
/// a NaN might produce an unexpected or non-portable result. See the [specification
/// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
/// if you need fully portable behavior (will return `false` for all NaNs).
///
/// ```
/// #![feature(f16)]
/// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let f = 7.0_f16;
/// let g = -7.0_f16;
///
/// assert!(f.is_sign_positive());
/// assert!(!g.is_sign_positive());
/// # }
/// ```
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
pub const fn is_sign_positive(self) -> bool {
!self.is_sign_negative()
}
/// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
/// negative sign bit and negative infinity.
///
/// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
/// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
/// conserved over arithmetic operations, the result of `is_sign_negative` on
/// a NaN might produce an unexpected or non-portable result. See the [specification
/// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
/// if you need fully portable behavior (will return `false` for all NaNs).
///
/// ```
/// #![feature(f16)]
/// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let f = 7.0_f16;
/// let g = -7.0_f16;
///
/// assert!(!f.is_sign_negative());
/// assert!(g.is_sign_negative());
/// # }
/// ```
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
pub const fn is_sign_negative(self) -> bool {
// IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
// applies to zeros and NaNs as well.
// SAFETY: This is just transmuting to get the sign bit, it's fine.
(self.to_bits() & (1 << 15)) != 0
}
/// Returns the least number greater than `self`.
///
/// Let `TINY` be the smallest representable positive `f16`. Then,
/// - if `self.is_nan()`, this returns `self`;
/// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
/// - if `self` is `-TINY`, this returns -0.0;
/// - if `self` is -0.0 or +0.0, this returns `TINY`;
/// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
/// - otherwise the unique least value greater than `self` is returned.
///
/// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
/// is finite `x == x.next_up().next_down()` also holds.
///
/// ```rust
/// #![feature(f16)]
/// # // FIXME(f16_f128): ABI issues on MSVC
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// // f16::EPSILON is the difference between 1.0 and the next number up.
/// assert_eq!(1.0f16.next_up(), 1.0 + f16::EPSILON);
/// // But not for most numbers.
/// assert!(0.1f16.next_up() < 0.1 + f16::EPSILON);
/// assert_eq!(4356f16.next_up(), 4360.0);
/// # }
/// ```
///
/// This operation corresponds to IEEE-754 `nextUp`.
///
/// [`NEG_INFINITY`]: Self::NEG_INFINITY
/// [`INFINITY`]: Self::INFINITY
/// [`MIN`]: Self::MIN
/// [`MAX`]: Self::MAX
#[inline]
#[doc(alias = "nextUp")]
#[unstable(feature = "f16", issue = "116909")]
pub const fn next_up(self) -> Self {
// Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
// denormals to zero. This is in general unsound and unsupported, but here
// we do our best to still produce the correct result on such targets.
let bits = self.to_bits();
if self.is_nan() || bits == Self::INFINITY.to_bits() {
return self;
}
let abs = bits & !Self::SIGN_MASK;
let next_bits = if abs == 0 {
Self::TINY_BITS
} else if bits == abs {
bits + 1
} else {
bits - 1
};
Self::from_bits(next_bits)
}
/// Returns the greatest number less than `self`.
///
/// Let `TINY` be the smallest representable positive `f16`. Then,
/// - if `self.is_nan()`, this returns `self`;
/// - if `self` is [`INFINITY`], this returns [`MAX`];
/// - if `self` is `TINY`, this returns 0.0;
/// - if `self` is -0.0 or +0.0, this returns `-TINY`;
/// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
/// - otherwise the unique greatest value less than `self` is returned.
///
/// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
/// is finite `x == x.next_down().next_up()` also holds.
///
/// ```rust
/// #![feature(f16)]
/// # // FIXME(f16_f128): ABI issues on MSVC
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let x = 1.0f16;
/// // Clamp value into range [0, 1).
/// let clamped = x.clamp(0.0, 1.0f16.next_down());
/// assert!(clamped < 1.0);
/// assert_eq!(clamped.next_up(), 1.0);
/// # }
/// ```
///
/// This operation corresponds to IEEE-754 `nextDown`.
///
/// [`NEG_INFINITY`]: Self::NEG_INFINITY
/// [`INFINITY`]: Self::INFINITY
/// [`MIN`]: Self::MIN
/// [`MAX`]: Self::MAX
#[inline]
#[doc(alias = "nextDown")]
#[unstable(feature = "f16", issue = "116909")]
pub const fn next_down(self) -> Self {
// Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
// denormals to zero. This is in general unsound and unsupported, but here
// we do our best to still produce the correct result on such targets.
let bits = self.to_bits();
if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
return self;
}
let abs = bits & !Self::SIGN_MASK;
let next_bits = if abs == 0 {
Self::NEG_TINY_BITS
} else if bits == abs {
bits - 1
} else {
bits + 1
};
Self::from_bits(next_bits)
}
/// Takes the reciprocal (inverse) of a number, `1/x`.
///
/// ```
/// #![feature(f16)]
/// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let x = 2.0_f16;
/// let abs_difference = (x.recip() - (1.0 / x)).abs();
///
/// assert!(abs_difference <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "this returns the result of the operation, without modifying the original"]
pub const fn recip(self) -> Self {
1.0 / self
}
/// Converts radians to degrees.
///
/// # 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)]
/// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let angle = std::f16::consts::PI;
///
/// let abs_difference = (angle.to_degrees() - 180.0).abs();
/// assert!(abs_difference <= 0.5);
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "this returns the result of the operation, without modifying the original"]
pub const fn to_degrees(self) -> Self {
// Use a literal to avoid double rounding, consts::PI is already rounded,
// and dividing would round again.
const PIS_IN_180: f16 = 57.2957795130823208767981548141051703_f16;
self * PIS_IN_180
}
/// Converts degrees to 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)]
/// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let angle = 180.0f16;
///
/// let abs_difference = (angle.to_radians() - std::f16::consts::PI).abs();
///
/// assert!(abs_difference <= 0.01);
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "this returns the result of the operation, without modifying the original"]
pub const fn to_radians(self) -> f16 {
// Use a literal to avoid double rounding, consts::PI is already rounded,
// and dividing would round again.
const RADS_PER_DEG: f16 = 0.017453292519943295769236907684886_f16;
self * RADS_PER_DEG
}
/// Returns the maximum of the two numbers, ignoring NaN.
///
/// If one of the arguments is NaN, then the other argument is returned.
/// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
/// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
/// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
/// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
///
/// ```
/// #![feature(f16)]
/// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
///
/// let x = 1.0f16;
/// let y = 2.0f16;
///
/// assert_eq!(x.max(y), y);
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "this returns the result of the comparison, without modifying either input"]
pub const fn max(self, other: f16) -> f16 {
intrinsics::maxnumf16(self, other)
}
/// Returns the minimum of the two numbers, ignoring NaN.
///
/// If one of the arguments is NaN, then the other argument is returned.
/// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
/// this function handles all NaNs the same way and avoids minNum's problems with associativity.
/// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
/// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
///
/// ```
/// #![feature(f16)]
/// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
///
/// let x = 1.0f16;
/// let y = 2.0f16;
///
/// assert_eq!(x.min(y), x);
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "this returns the result of the comparison, without modifying either input"]
pub const fn min(self, other: f16) -> f16 {
intrinsics::minnumf16(self, other)
}
/// Returns the maximum of the two numbers, propagating NaN.
///
/// This returns NaN when *either* argument is NaN, as opposed to
/// [`f16::max`] which only returns NaN when *both* arguments are NaN.
///
/// ```
/// #![feature(f16)]
/// #![feature(float_minimum_maximum)]
/// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
///
/// let x = 1.0f16;
/// let y = 2.0f16;
///
/// assert_eq!(x.maximum(y), y);
/// assert!(x.maximum(f16::NAN).is_nan());
/// # }
/// ```
///
/// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
/// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
/// Note that this follows the semantics specified in IEEE 754-2019.
///
/// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
/// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
#[inline]
#[unstable(feature = "f16", issue = "116909")]
// #[unstable(feature = "float_minimum_maximum", issue = "91079")]
#[must_use = "this returns the result of the comparison, without modifying either input"]
pub const fn maximum(self, other: f16) -> f16 {
intrinsics::maximumf16(self, other)
}
/// Returns the minimum of the two numbers, propagating NaN.
///
/// This returns NaN when *either* argument is NaN, as opposed to
/// [`f16::min`] which only returns NaN when *both* arguments are NaN.
///
/// ```
/// #![feature(f16)]
/// #![feature(float_minimum_maximum)]
/// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
///
/// let x = 1.0f16;
/// let y = 2.0f16;
///
/// assert_eq!(x.minimum(y), x);
/// assert!(x.minimum(f16::NAN).is_nan());
/// # }
/// ```
///
/// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
/// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
/// Note that this follows the semantics specified in IEEE 754-2019.
///
/// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
/// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
#[inline]
#[unstable(feature = "f16", issue = "116909")]
// #[unstable(feature = "float_minimum_maximum", issue = "91079")]
#[must_use = "this returns the result of the comparison, without modifying either input"]
pub const fn minimum(self, other: f16) -> f16 {
intrinsics::minimumf16(self, other)
}
/// Calculates the midpoint (average) between `self` and `rhs`.
///
/// This returns NaN when *either* argument is NaN or if a combination of
/// +inf and -inf is provided as arguments.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(target_arch = "aarch64")] { // FIXME(f16_F128): rust-lang/rust#123885
///
/// assert_eq!(1f16.midpoint(4.0), 2.5);
/// assert_eq!((-5.5f16).midpoint(8.0), 1.25);
/// # }
/// ```
#[inline]
#[doc(alias = "average")]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
pub const fn midpoint(self, other: f16) -> f16 {
const LO: f16 = f16::MIN_POSITIVE * 2.;
const HI: f16 = f16::MAX / 2.;
let (a, b) = (self, other);
let abs_a = a.abs();
let abs_b = b.abs();
if abs_a <= HI && abs_b <= HI {
// Overflow is impossible
(a + b) / 2.
} else if abs_a < LO {
// Not safe to halve `a` (would underflow)
a + (b / 2.)
} else if abs_b < LO {
// Not safe to halve `b` (would underflow)
(a / 2.) + b
} else {
// Safe to halve `a` and `b`
(a / 2.) + (b / 2.)
}
}
/// Rounds toward zero and converts to any primitive integer type,
/// assuming that the value is finite and fits in that type.
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let value = 4.6_f16;
/// let rounded = unsafe { value.to_int_unchecked::<u16>() };
/// assert_eq!(rounded, 4);
///
/// let value = -128.9_f16;
/// let rounded = unsafe { value.to_int_unchecked::<i8>() };
/// assert_eq!(rounded, i8::MIN);
/// # }
/// ```
///
/// # Safety
///
/// The value must:
///
/// * Not be `NaN`
/// * Not be infinite
/// * Be representable in the return type `Int`, after truncating off its fractional part
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "this returns the result of the operation, without modifying the original"]
pub unsafe fn to_int_unchecked<Int>(self) -> Int
where
Self: FloatToInt<Int>,
{
// SAFETY: the caller must uphold the safety contract for
// `FloatToInt::to_int_unchecked`.
unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
}
/// Raw transmutation to `u16`.
///
/// This is currently identical to `transmute::<f16, u16>(self)` on all platforms.
///
/// See [`from_bits`](#method.from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// Note that this function is distinct from `as` casting, which attempts to
/// preserve the *numeric* value, and not the bitwise value.
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// # // FIXME(f16_f128): enable this once const casting works
/// # // assert_ne!((1f16).to_bits(), 1f16 as u128); // to_bits() is not casting!
/// assert_eq!((12.5f16).to_bits(), 0x4a40);
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "this returns the result of the operation, without modifying the original"]
#[allow(unnecessary_transmutes)]
pub const fn to_bits(self) -> u16 {
// SAFETY: `u16` is a plain old datatype so we can always transmute to it.
unsafe { mem::transmute(self) }
}
/// Raw transmutation from `u16`.
///
/// This is currently identical to `transmute::<u16, f16>(v)` on all platforms.
/// It turns out this is incredibly portable, for two reasons:
///
/// * Floats and Ints have the same endianness on all supported platforms.
/// * IEEE 754 very precisely specifies the bit layout of floats.
///
/// However there is one caveat: prior to the 2008 version of IEEE 754, how
/// to interpret the NaN signaling bit wasn't actually specified. Most platforms
/// (notably x86 and ARM) picked the interpretation that was ultimately
/// standardized in 2008, but some didn't (notably MIPS). As a result, all
/// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
///
/// Rather than trying to preserve signaling-ness cross-platform, this
/// implementation favors preserving the exact bits. This means that
/// any payloads encoded in NaNs will be preserved even if the result of
/// this method is sent over the network from an x86 machine to a MIPS one.
///
/// If the results of this method are only manipulated by the same
/// architecture that produced them, then there is no portability concern.
///
/// If the input isn't NaN, then there is no portability concern.
///
/// If you don't care about signalingness (very likely), then there is no
/// portability concern.
///
/// Note that this function is distinct from `as` casting, which attempts to
/// preserve the *numeric* value, and not the bitwise value.
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let v = f16::from_bits(0x4a40);
/// assert_eq!(v, 12.5);
/// # }
/// ```
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
#[allow(unnecessary_transmutes)]
pub const fn from_bits(v: u16) -> Self {
// It turns out the safety issues with sNaN were overblown! Hooray!
// SAFETY: `u16` is a plain old datatype so we can always transmute from it.
unsafe { mem::transmute(v) }
}
/// Returns the memory representation of this floating point number as a byte array in
/// big-endian (network) byte order.
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let bytes = 12.5f16.to_be_bytes();
/// assert_eq!(bytes, [0x4a, 0x40]);
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "this returns the result of the operation, without modifying the original"]
pub const fn to_be_bytes(self) -> [u8; 2] {
self.to_bits().to_be_bytes()
}
/// Returns the memory representation of this floating point number as a byte array in
/// little-endian byte order.
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let bytes = 12.5f16.to_le_bytes();
/// assert_eq!(bytes, [0x40, 0x4a]);
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "this returns the result of the operation, without modifying the original"]
pub const fn to_le_bytes(self) -> [u8; 2] {
self.to_bits().to_le_bytes()
}
/// Returns the memory representation of this floating point number as a byte array in
/// native byte order.
///
/// As the target platform's native endianness is used, portable code
/// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
///
/// [`to_be_bytes`]: f16::to_be_bytes
/// [`to_le_bytes`]: f16::to_le_bytes
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # // FIXME(f16_f128): LLVM crashes on s390x, llvm/llvm-project#50374
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let bytes = 12.5f16.to_ne_bytes();
/// assert_eq!(
/// bytes,
/// if cfg!(target_endian = "big") {
/// [0x4a, 0x40]
/// } else {
/// [0x40, 0x4a]
/// }
/// );
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "this returns the result of the operation, without modifying the original"]
pub const fn to_ne_bytes(self) -> [u8; 2] {
self.to_bits().to_ne_bytes()
}
/// Creates a floating point value from its representation as a byte array in big endian.
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let value = f16::from_be_bytes([0x4a, 0x40]);
/// assert_eq!(value, 12.5);
/// # }
/// ```
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
pub const fn from_be_bytes(bytes: [u8; 2]) -> Self {
Self::from_bits(u16::from_be_bytes(bytes))
}
/// Creates a floating point value from its representation as a byte array in little endian.
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let value = f16::from_le_bytes([0x40, 0x4a]);
/// assert_eq!(value, 12.5);
/// # }
/// ```
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
pub const fn from_le_bytes(bytes: [u8; 2]) -> Self {
Self::from_bits(u16::from_le_bytes(bytes))
}
/// Creates a floating point value from its representation as a byte array in native endian.
///
/// As the target platform's native endianness is used, portable code
/// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
/// appropriate instead.
///
/// [`from_be_bytes`]: f16::from_be_bytes
/// [`from_le_bytes`]: f16::from_le_bytes
///
/// See [`from_bits`](Self::from_bits) for some discussion of the
/// portability of this operation (there are almost no issues).
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let value = f16::from_ne_bytes(if cfg!(target_endian = "big") {
/// [0x4a, 0x40]
/// } else {
/// [0x40, 0x4a]
/// });
/// assert_eq!(value, 12.5);
/// # }
/// ```
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
pub const fn from_ne_bytes(bytes: [u8; 2]) -> Self {
Self::from_bits(u16::from_ne_bytes(bytes))
}
/// Returns the ordering between `self` and `other`.
///
/// Unlike the standard partial comparison between floating point numbers,
/// this comparison always produces an ordering in accordance to
/// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
/// floating point standard. The values are ordered in the following sequence:
///
/// - negative quiet NaN
/// - negative signaling NaN
/// - negative infinity
/// - negative numbers
/// - negative subnormal numbers
/// - negative zero
/// - positive zero
/// - positive subnormal numbers
/// - positive numbers
/// - positive infinity
/// - positive signaling NaN
/// - positive quiet NaN.
///
/// The ordering established by this function does not always agree with the
/// [`PartialOrd`] and [`PartialEq`] implementations of `f16`. For example,
/// they consider negative and positive zero equal, while `total_cmp`
/// doesn't.
///
/// The interpretation of the signaling NaN bit follows the definition in
/// the IEEE 754 standard, which may not match the interpretation by some of
/// the older, non-conformant (e.g. MIPS) hardware implementations.
///
/// # Example
///
/// ```
/// #![feature(f16)]
/// # // FIXME(f16_f128): extendhfsf2, truncsfhf2, __gnu_h2f_ieee, __gnu_f2h_ieee missing for many platforms
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// struct GoodBoy {
/// name: &'static str,
/// weight: f16,
/// }
///
/// let mut bois = vec![
/// GoodBoy { name: "Pucci", weight: 0.1 },
/// GoodBoy { name: "Woofer", weight: 99.0 },
/// GoodBoy { name: "Yapper", weight: 10.0 },
/// GoodBoy { name: "Chonk", weight: f16::INFINITY },
/// GoodBoy { name: "Abs. Unit", weight: f16::NAN },
/// GoodBoy { name: "Floaty", weight: -5.0 },
/// ];
///
/// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
///
/// // `f16::NAN` could be positive or negative, which will affect the sort order.
/// if f16::NAN.is_sign_negative() {
/// bois.into_iter().map(|b| b.weight)
/// .zip([f16::NAN, -5.0, 0.1, 10.0, 99.0, f16::INFINITY].iter())
/// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
/// } else {
/// bois.into_iter().map(|b| b.weight)
/// .zip([-5.0, 0.1, 10.0, 99.0, f16::INFINITY, f16::NAN].iter())
/// .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
/// }
/// # }
/// ```
#[inline]
#[must_use]
#[unstable(feature = "f16", issue = "116909")]
pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
let mut left = self.to_bits() as i16;
let mut right = other.to_bits() as i16;
// In case of negatives, flip all the bits except the sign
// to achieve a similar layout as two's complement integers
//
// Why does this work? IEEE 754 floats consist of three fields:
// Sign bit, exponent and mantissa. The set of exponent and mantissa
// fields as a whole have the property that their bitwise order is
// equal to the numeric magnitude where the magnitude is defined.
// The magnitude is not normally defined on NaN values, but
// IEEE 754 totalOrder defines the NaN values also to follow the
// bitwise order. This leads to order explained in the doc comment.
// However, the representation of magnitude is the same for negative
// and positive numbers – only the sign bit is different.
// To easily compare the floats as signed integers, we need to
// flip the exponent and mantissa bits in case of negative numbers.
// We effectively convert the numbers to "two's complement" form.
//
// To do the flipping, we construct a mask and XOR against it.
// We branchlessly calculate an "all-ones except for the sign bit"
// mask from negative-signed values: right shifting sign-extends
// the integer, so we "fill" the mask with sign bits, and then
// convert to unsigned to push one more zero bit.
// On positive values, the mask is all zeros, so it's a no-op.
left ^= (((left >> 15) as u16) >> 1) as i16;
right ^= (((right >> 15) as u16) >> 1) as i16;
left.cmp(&right)
}
/// Restrict a value to a certain interval unless it is NaN.
///
/// Returns `max` if `self` is greater than `max`, and `min` if `self` is
/// less than `min`. Otherwise this returns `self`.
///
/// Note that this function returns NaN if the initial value was NaN as
/// well.
///
/// # Panics
///
/// Panics if `min > max`, `min` is NaN, or `max` is NaN.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// assert!((-3.0f16).clamp(-2.0, 1.0) == -2.0);
/// assert!((0.0f16).clamp(-2.0, 1.0) == 0.0);
/// assert!((2.0f16).clamp(-2.0, 1.0) == 1.0);
/// assert!((f16::NAN).clamp(-2.0, 1.0).is_nan());
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub const fn clamp(mut self, min: f16, max: f16) -> f16 {
const_assert!(
min <= max,
"min > max, or either was NaN",
"min > max, or either was NaN. min = {min:?}, max = {max:?}",
min: f16,
max: f16,
);
if self < min {
self = min;
}
if self > max {
self = max;
}
self
}
/// Computes the absolute value of `self`.
///
/// This function always returns the precise result.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let x = 3.5_f16;
/// let y = -3.5_f16;
///
/// assert_eq!(x.abs(), x);
/// assert_eq!(y.abs(), -y);
///
/// assert!(f16::NAN.abs().is_nan());
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub const fn abs(self) -> Self {
// FIXME(f16_f128): replace with `intrinsics::fabsf16` when available
Self::from_bits(self.to_bits() & !(1 << 15))
}
/// 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
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let f = 3.5_f16;
///
/// assert_eq!(f.signum(), 1.0);
/// assert_eq!(f16::NEG_INFINITY.signum(), -1.0);
///
/// assert!(f16::NAN.signum().is_nan());
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub const fn signum(self) -> f16 {
if self.is_nan() { Self::NAN } else { 1.0_f16.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 same payload as `self` and the sign bit of `sign` is
/// returned.
///
/// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
/// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
/// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
/// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
/// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
/// info.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
///
/// let f = 3.5_f16;
///
/// assert_eq!(f.copysign(0.42), 3.5_f16);
/// assert_eq!(f.copysign(-0.42), -3.5_f16);
/// assert_eq!((-f).copysign(0.42), 3.5_f16);
/// assert_eq!((-f).copysign(-0.42), -3.5_f16);
///
/// assert!(f16::NAN.copysign(1.0).is_nan());
/// # }
/// ```
#[inline]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub const fn copysign(self, sign: f16) -> f16 {
// SAFETY: this is actually a safe intrinsic
unsafe { intrinsics::copysignf16(self, sign) }
}
/// Float addition that allows optimizations based on algebraic rules.
///
/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
#[must_use = "method returns a new number and does not mutate the original value"]
#[unstable(feature = "float_algebraic", issue = "136469")]
#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
#[inline]
pub const fn algebraic_add(self, rhs: f16) -> f16 {
intrinsics::fadd_algebraic(self, rhs)
}
/// Float subtraction that allows optimizations based on algebraic rules.
///
/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
#[must_use = "method returns a new number and does not mutate the original value"]
#[unstable(feature = "float_algebraic", issue = "136469")]
#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
#[inline]
pub const fn algebraic_sub(self, rhs: f16) -> f16 {
intrinsics::fsub_algebraic(self, rhs)
}
/// Float multiplication that allows optimizations based on algebraic rules.
///
/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
#[must_use = "method returns a new number and does not mutate the original value"]
#[unstable(feature = "float_algebraic", issue = "136469")]
#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
#[inline]
pub const fn algebraic_mul(self, rhs: f16) -> f16 {
intrinsics::fmul_algebraic(self, rhs)
}
/// Float division that allows optimizations based on algebraic rules.
///
/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
#[must_use = "method returns a new number and does not mutate the original value"]
#[unstable(feature = "float_algebraic", issue = "136469")]
#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
#[inline]
pub const fn algebraic_div(self, rhs: f16) -> f16 {
intrinsics::fdiv_algebraic(self, rhs)
}
/// Float remainder that allows optimizations based on algebraic rules.
///
/// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
#[must_use = "method returns a new number and does not mutate the original value"]
#[unstable(feature = "float_algebraic", issue = "136469")]
#[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
#[inline]
pub const fn algebraic_rem(self, rhs: f16) -> f16 {
intrinsics::frem_algebraic(self, rhs)
}
}
// Functions in this module fall into `core_float_math`
// #[unstable(feature = "core_float_math", issue = "137578")]
#[cfg(not(test))]
#[doc(test(attr(feature(cfg_target_has_reliable_f16_f128), expect(internal_features))))]
impl f16 {
/// Returns the largest integer less than or equal to `self`.
///
/// This function always returns the precise result.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let f = 3.7_f16;
/// let g = 3.0_f16;
/// let h = -3.7_f16;
///
/// assert_eq!(f.floor(), 3.0);
/// assert_eq!(g.floor(), 3.0);
/// assert_eq!(h.floor(), -4.0);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub const fn floor(self) -> f16 {
// SAFETY: intrinsic with no preconditions
unsafe { intrinsics::floorf16(self) }
}
/// Returns the smallest integer greater than or equal to `self`.
///
/// This function always returns the precise result.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let f = 3.01_f16;
/// let g = 4.0_f16;
///
/// assert_eq!(f.ceil(), 4.0);
/// assert_eq!(g.ceil(), 4.0);
/// # }
/// ```
#[inline]
#[doc(alias = "ceiling")]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub const fn ceil(self) -> f16 {
// SAFETY: intrinsic with no preconditions
unsafe { intrinsics::ceilf16(self) }
}
/// Returns the nearest integer to `self`. If a value is half-way between two
/// integers, round away from `0.0`.
///
/// This function always returns the precise result.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let f = 3.3_f16;
/// let g = -3.3_f16;
/// let h = -3.7_f16;
/// let i = 3.5_f16;
/// let j = 4.5_f16;
///
/// assert_eq!(f.round(), 3.0);
/// assert_eq!(g.round(), -3.0);
/// assert_eq!(h.round(), -4.0);
/// assert_eq!(i.round(), 4.0);
/// assert_eq!(j.round(), 5.0);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub const fn round(self) -> f16 {
// SAFETY: intrinsic with no preconditions
unsafe { intrinsics::roundf16(self) }
}
/// Returns the nearest integer to a number. Rounds half-way cases to the number
/// with an even least significant digit.
///
/// This function always returns the precise result.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let f = 3.3_f16;
/// let g = -3.3_f16;
/// let h = 3.5_f16;
/// let i = 4.5_f16;
///
/// assert_eq!(f.round_ties_even(), 3.0);
/// assert_eq!(g.round_ties_even(), -3.0);
/// assert_eq!(h.round_ties_even(), 4.0);
/// assert_eq!(i.round_ties_even(), 4.0);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub const fn round_ties_even(self) -> f16 {
intrinsics::round_ties_even_f16(self)
}
/// Returns the integer part of `self`.
/// This means that non-integer numbers are always truncated towards zero.
///
/// This function always returns the precise result.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let f = 3.7_f16;
/// let g = 3.0_f16;
/// let h = -3.7_f16;
///
/// assert_eq!(f.trunc(), 3.0);
/// assert_eq!(g.trunc(), 3.0);
/// assert_eq!(h.trunc(), -3.0);
/// # }
/// ```
#[inline]
#[doc(alias = "truncate")]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub const fn trunc(self) -> f16 {
// SAFETY: intrinsic with no preconditions
unsafe { intrinsics::truncf16(self) }
}
/// Returns the fractional part of `self`.
///
/// This function always returns the precise result.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let x = 3.6_f16;
/// let y = -3.6_f16;
/// let abs_difference_x = (x.fract() - 0.6).abs();
/// let abs_difference_y = (y.fract() - (-0.6)).abs();
///
/// assert!(abs_difference_x <= f16::EPSILON);
/// assert!(abs_difference_y <= f16::EPSILON);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[rustc_const_unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub const fn fract(self) -> f16 {
self - self.trunc()
}
/// 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.
///
/// # Precision
///
/// The result of this operation is guaranteed to be the rounded
/// infinite-precision result. It is specified by IEEE 754 as
/// `fusedMultiplyAdd` and guaranteed not to change.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let m = 10.0_f16;
/// let x = 4.0_f16;
/// let b = 60.0_f16;
///
/// assert_eq!(m.mul_add(x, b), 100.0);
/// assert_eq!(m * x + b, 100.0);
///
/// let one_plus_eps = 1.0_f16 + f16::EPSILON;
/// let one_minus_eps = 1.0_f16 - f16::EPSILON;
/// let minus_one = -1.0_f16;
///
/// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
/// assert_eq!(one_plus_eps.mul_add(one_minus_eps, minus_one), -f16::EPSILON * f16::EPSILON);
/// // Different rounding with the non-fused multiply and add.
/// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[unstable(feature = "f16", issue = "116909")]
#[doc(alias = "fmaf16", alias = "fusedMultiplyAdd")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn mul_add(self, a: f16, b: f16) -> f16 {
// SAFETY: intrinsic with no preconditions
unsafe { intrinsics::fmaf16(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`.
///
/// # Precision
///
/// The result of this operation is guaranteed to be the rounded
/// infinite-precision result.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let a: f16 = 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
/// # }
/// ```
#[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 div_euclid(self, rhs: f16) -> f16 {
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)`
/// approximately.
///
/// # Precision
///
/// The result of this operation is guaranteed to be the rounded
/// infinite-precision result.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let a: f16 = 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!((-f16::EPSILON).rem_euclid(3.0) != 0.0);
/// # }
/// ```
#[inline]
#[rustc_allow_incoherent_impl]
#[doc(alias = "modulo", alias = "mod")]
#[unstable(feature = "f16", issue = "116909")]
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn rem_euclid(self, rhs: f16) -> f16 {
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.
///
/// # 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.powi(2) - (x * x)).abs();
/// assert!(abs_difference <= f16::EPSILON);
///
/// assert_eq!(f16::powi(f16::NAN, 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 powi(self, n: i32) -> f16 {
// SAFETY: intrinsic with no preconditions
unsafe { intrinsics::powif16(self, n) }
}
/// Returns the square root of a number.
///
/// Returns NaN if `self` is a negative number other than `-0.0`.
///
/// # Precision
///
/// The result of this operation is guaranteed to be the rounded
/// infinite-precision result. It is specified by IEEE 754 as `squareRoot`
/// and guaranteed not to change.
///
/// # Examples
///
/// ```
/// #![feature(f16)]
/// # #[cfg(not(miri))]
/// # #[cfg(target_has_reliable_f16_math)] {
///
/// let positive = 4.0_f16;
/// let negative = -4.0_f16;
/// let negative_zero = -0.0_f16;
///
/// assert_eq!(positive.sqrt(), 2.0);
/// assert!(negative.sqrt().is_nan());
/// assert!(negative_zero.sqrt() == negative_zero);
/// # }
/// ```
#[inline]
#[doc(alias = "squareRoot")]
#[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 sqrt(self) -> f16 {
// SAFETY: intrinsic with no preconditions
unsafe { intrinsics::sqrtf16(self) }
}
/// Returns the cube root of a number.
///
/// # 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 `cbrtf` 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 = 8.0f16;
///
/// // x^(1/3) - 2 == 0
/// let abs_difference = (x.cbrt() - 2.0).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 cbrt(self) -> f16 {
libm::cbrtf(self as f32) as f16
}
}