mirror of
https://github.com/rust-lang/rust.git
synced 2026-04-26 13:01:27 +03:00
Jacob Pratt
b3ccc964d5
Exposing Float Masks Tracking issue: rust-lang/rust#154064 ACP: rust-lang/libs-team#753
2021 lines
73 KiB
Rust
2021 lines
73 KiB
Rust
//! Constants for the `f16` half-precision floating point type.
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//!
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//! *[See also the `f16` primitive type][f16].*
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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 `f16` type.
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#![unstable(feature = "f16", issue = "116909")]
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use crate::convert::FloatToInt;
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use crate::num::FpCategory;
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#[cfg(not(test))]
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use crate::num::imp::libm;
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use crate::panic::const_assert;
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use crate::{intrinsics, mem};
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/// Basic mathematical constants.
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#[unstable(feature = "f16", issue = "116909")]
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#[rustc_diagnostic_item = "f16_consts_mod"]
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pub mod consts {
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// FIXME: replace with mathematical constants from cmath.
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/// Archimedes' constant (π)
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#[unstable(feature = "f16", issue = "116909")]
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pub const PI: f16 = 3.14159265358979323846264338327950288_f16;
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/// The full circle constant (τ)
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///
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/// Equal to 2π.
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#[unstable(feature = "f16", issue = "116909")]
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pub const TAU: f16 = 6.28318530717958647692528676655900577_f16;
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/// The golden ratio (φ)
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#[unstable(feature = "f16", issue = "116909")]
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pub const GOLDEN_RATIO: f16 = 1.618033988749894848204586834365638118_f16;
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/// The Euler-Mascheroni constant (γ)
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#[unstable(feature = "f16", issue = "116909")]
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pub const EULER_GAMMA: f16 = 0.577215664901532860606512090082402431_f16;
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/// π/2
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#[unstable(feature = "f16", issue = "116909")]
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pub const FRAC_PI_2: f16 = 1.57079632679489661923132169163975144_f16;
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/// π/3
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#[unstable(feature = "f16", issue = "116909")]
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pub const FRAC_PI_3: f16 = 1.04719755119659774615421446109316763_f16;
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/// π/4
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#[unstable(feature = "f16", issue = "116909")]
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pub const FRAC_PI_4: f16 = 0.785398163397448309615660845819875721_f16;
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/// π/6
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#[unstable(feature = "f16", issue = "116909")]
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pub const FRAC_PI_6: f16 = 0.52359877559829887307710723054658381_f16;
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/// π/8
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#[unstable(feature = "f16", issue = "116909")]
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pub const FRAC_PI_8: f16 = 0.39269908169872415480783042290993786_f16;
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/// 1/π
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#[unstable(feature = "f16", issue = "116909")]
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pub const FRAC_1_PI: f16 = 0.318309886183790671537767526745028724_f16;
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/// 1/sqrt(π)
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#[unstable(feature = "f16", issue = "116909")]
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// Also, #[unstable(feature = "more_float_constants", issue = "146939")]
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pub const FRAC_1_SQRT_PI: f16 = 0.564189583547756286948079451560772586_f16;
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/// 1/sqrt(2π)
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#[doc(alias = "FRAC_1_SQRT_TAU")]
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#[unstable(feature = "f16", issue = "116909")]
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// Also, #[unstable(feature = "more_float_constants", issue = "146939")]
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pub const FRAC_1_SQRT_2PI: f16 = 0.398942280401432677939946059934381868_f16;
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/// 2/π
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#[unstable(feature = "f16", issue = "116909")]
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pub const FRAC_2_PI: f16 = 0.636619772367581343075535053490057448_f16;
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/// 2/sqrt(π)
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#[unstable(feature = "f16", issue = "116909")]
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pub const FRAC_2_SQRT_PI: f16 = 1.12837916709551257389615890312154517_f16;
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/// sqrt(2)
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#[unstable(feature = "f16", issue = "116909")]
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pub const SQRT_2: f16 = 1.41421356237309504880168872420969808_f16;
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/// 1/sqrt(2)
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#[unstable(feature = "f16", issue = "116909")]
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pub const FRAC_1_SQRT_2: f16 = 0.707106781186547524400844362104849039_f16;
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/// sqrt(3)
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#[unstable(feature = "f16", issue = "116909")]
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// Also, #[unstable(feature = "more_float_constants", issue = "146939")]
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pub const SQRT_3: f16 = 1.732050807568877293527446341505872367_f16;
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/// 1/sqrt(3)
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#[unstable(feature = "f16", issue = "116909")]
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// Also, #[unstable(feature = "more_float_constants", issue = "146939")]
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pub const FRAC_1_SQRT_3: f16 = 0.577350269189625764509148780501957456_f16;
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/// sqrt(5)
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#[unstable(feature = "more_float_constants", issue = "146939")]
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// Also, #[unstable(feature = "f16", issue = "116909")]
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pub const SQRT_5: f16 = 2.23606797749978969640917366873127623_f16;
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/// 1/sqrt(5)
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#[unstable(feature = "more_float_constants", issue = "146939")]
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// Also, #[unstable(feature = "f16", issue = "116909")]
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pub const FRAC_1_SQRT_5: f16 = 0.44721359549995793928183473374625524_f16;
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/// Euler's number (e)
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#[unstable(feature = "f16", issue = "116909")]
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pub const E: f16 = 2.71828182845904523536028747135266250_f16;
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/// log<sub>2</sub>(10)
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#[unstable(feature = "f16", issue = "116909")]
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pub const LOG2_10: f16 = 3.32192809488736234787031942948939018_f16;
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/// log<sub>2</sub>(e)
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#[unstable(feature = "f16", issue = "116909")]
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pub const LOG2_E: f16 = 1.44269504088896340735992468100189214_f16;
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/// log<sub>10</sub>(2)
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#[unstable(feature = "f16", issue = "116909")]
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pub const LOG10_2: f16 = 0.301029995663981195213738894724493027_f16;
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/// log<sub>10</sub>(e)
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#[unstable(feature = "f16", issue = "116909")]
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pub const LOG10_E: f16 = 0.434294481903251827651128918916605082_f16;
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/// ln(2)
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#[unstable(feature = "f16", issue = "116909")]
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pub const LN_2: f16 = 0.693147180559945309417232121458176568_f16;
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/// ln(10)
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#[unstable(feature = "f16", issue = "116909")]
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pub const LN_10: f16 = 2.30258509299404568401799145468436421_f16;
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}
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#[doc(test(attr(
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feature(cfg_target_has_reliable_f16_f128),
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allow(internal_features, unused_features)
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)))]
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impl f16 {
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/// The radix or base of the internal representation of `f16`.
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#[unstable(feature = "f16", issue = "116909")]
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pub const RADIX: u32 = 2;
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/// The size of this float type in bits.
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// #[unstable(feature = "f16", issue = "116909")]
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#[unstable(feature = "float_bits_const", issue = "151073")]
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pub const BITS: u32 = 16;
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/// Number of significant digits in base 2.
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///
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/// Note that the size of the mantissa in the bitwise representation is one
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/// smaller than this since the leading 1 is not stored explicitly.
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#[unstable(feature = "f16", issue = "116909")]
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pub const MANTISSA_DIGITS: u32 = 11;
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/// Approximate number of significant digits in base 10.
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///
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/// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
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/// significant digits can be converted to `f16` and back without loss.
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///
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/// Equal to floor(log<sub>10</sub> 2<sup>[`MANTISSA_DIGITS`] − 1</sup>).
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///
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/// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
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#[unstable(feature = "f16", issue = "116909")]
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pub const DIGITS: u32 = 3;
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/// [Machine epsilon] value for `f16`.
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///
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/// This is the difference between `1.0` and the next larger representable number.
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///
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/// Equal to 2<sup>1 − [`MANTISSA_DIGITS`]</sup>.
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///
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/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
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/// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
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#[unstable(feature = "f16", issue = "116909")]
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#[rustc_diagnostic_item = "f16_epsilon"]
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pub const EPSILON: f16 = 9.7656e-4_f16;
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/// Smallest finite `f16` value.
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///
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/// Equal to −[`MAX`].
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///
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/// [`MAX`]: f16::MAX
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#[unstable(feature = "f16", issue = "116909")]
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pub const MIN: f16 = -6.5504e+4_f16;
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/// Smallest positive normal `f16` value.
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///
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/// Equal to 2<sup>[`MIN_EXP`] − 1</sup>.
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///
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/// [`MIN_EXP`]: f16::MIN_EXP
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#[unstable(feature = "f16", issue = "116909")]
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pub const MIN_POSITIVE: f16 = 6.1035e-5_f16;
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/// Largest finite `f16` value.
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///
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/// Equal to
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/// (1 − 2<sup>−[`MANTISSA_DIGITS`]</sup>) 2<sup>[`MAX_EXP`]</sup>.
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///
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/// [`MANTISSA_DIGITS`]: f16::MANTISSA_DIGITS
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/// [`MAX_EXP`]: f16::MAX_EXP
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#[unstable(feature = "f16", issue = "116909")]
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pub const MAX: f16 = 6.5504e+4_f16;
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/// One greater than the minimum possible *normal* power of 2 exponent
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/// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
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///
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/// This corresponds to the exact minimum possible *normal* power of 2 exponent
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/// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
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/// In other words, all normal numbers representable by this type are
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/// greater than or equal to 0.5 × 2<sup><i>MIN_EXP</i></sup>.
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#[unstable(feature = "f16", issue = "116909")]
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pub const MIN_EXP: i32 = -13;
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/// One greater than the maximum possible power of 2 exponent
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/// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
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///
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/// This corresponds to the exact maximum possible power of 2 exponent
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/// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
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/// In other words, all numbers representable by this type are
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/// strictly less than 2<sup><i>MAX_EXP</i></sup>.
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#[unstable(feature = "f16", issue = "116909")]
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pub const MAX_EXP: i32 = 16;
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/// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
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///
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/// Equal to ceil(log<sub>10</sub> [`MIN_POSITIVE`]).
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///
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/// [`MIN_POSITIVE`]: f16::MIN_POSITIVE
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#[unstable(feature = "f16", issue = "116909")]
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pub const MIN_10_EXP: i32 = -4;
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/// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
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///
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/// Equal to floor(log<sub>10</sub> [`MAX`]).
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///
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/// [`MAX`]: f16::MAX
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#[unstable(feature = "f16", issue = "116909")]
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pub const MAX_10_EXP: i32 = 4;
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/// Not a Number (NaN).
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///
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/// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
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/// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
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/// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
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/// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
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/// info.
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///
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/// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
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/// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
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/// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
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/// The concrete bit pattern may change across Rust versions and target platforms.
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#[allow(clippy::eq_op)]
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#[rustc_diagnostic_item = "f16_nan"]
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#[unstable(feature = "f16", issue = "116909")]
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pub const NAN: f16 = 0.0_f16 / 0.0_f16;
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/// Infinity (∞).
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#[unstable(feature = "f16", issue = "116909")]
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pub const INFINITY: f16 = 1.0_f16 / 0.0_f16;
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/// Negative infinity (−∞).
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#[unstable(feature = "f16", issue = "116909")]
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pub const NEG_INFINITY: f16 = -1.0_f16 / 0.0_f16;
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/// Maximum integer that can be represented exactly in an [`f16`] value,
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/// with no other integer converting to the same floating point value.
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///
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/// For an integer `x` which satisfies `MIN_EXACT_INTEGER <= x <= MAX_EXACT_INTEGER`,
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/// there is a "one-to-one" mapping between [`i16`] and [`f16`] values.
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/// `MAX_EXACT_INTEGER + 1` also converts losslessly to [`f16`] and back to
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/// [`i16`], but `MAX_EXACT_INTEGER + 2` converts to the same [`f16`] value
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/// (and back to `MAX_EXACT_INTEGER + 1` as an integer) so there is not a
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/// "one-to-one" mapping.
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///
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/// [`MAX_EXACT_INTEGER`]: f16::MAX_EXACT_INTEGER
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/// [`MIN_EXACT_INTEGER`]: f16::MIN_EXACT_INTEGER
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/// ```
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/// #![feature(f16)]
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/// #![feature(float_exact_integer_constants)]
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/// # // FIXME(#152635): Float rounding on `i586` does not adhere to IEEE 754
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/// # #[cfg(not(all(target_arch = "x86", not(target_feature = "sse"))))] {
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/// # #[cfg(target_has_reliable_f16)] {
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/// let max_exact_int = f16::MAX_EXACT_INTEGER;
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/// assert_eq!(max_exact_int, max_exact_int as f16 as i16);
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/// assert_eq!(max_exact_int + 1, (max_exact_int + 1) as f16 as i16);
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/// assert_ne!(max_exact_int + 2, (max_exact_int + 2) as f16 as i16);
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///
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/// // Beyond `f16::MAX_EXACT_INTEGER`, multiple integers can map to one float value
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/// assert_eq!((max_exact_int + 1) as f16, (max_exact_int + 2) as f16);
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/// # }}
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/// ```
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// #[unstable(feature = "f16", issue = "116909")]
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#[unstable(feature = "float_exact_integer_constants", issue = "152466")]
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pub const MAX_EXACT_INTEGER: i16 = (1 << Self::MANTISSA_DIGITS) - 1;
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/// Minimum integer that can be represented exactly in an [`f16`] value,
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/// with no other integer converting to the same floating point value.
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///
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/// For an integer `x` which satisfies `MIN_EXACT_INTEGER <= x <= MAX_EXACT_INTEGER`,
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/// there is a "one-to-one" mapping between [`i16`] and [`f16`] values.
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/// `MAX_EXACT_INTEGER + 1` also converts losslessly to [`f16`] and back to
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/// [`i16`], but `MAX_EXACT_INTEGER + 2` converts to the same [`f16`] value
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/// (and back to `MAX_EXACT_INTEGER + 1` as an integer) so there is not a
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/// "one-to-one" mapping.
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///
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/// This constant is equivalent to `-MAX_EXACT_INTEGER`.
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///
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/// [`MAX_EXACT_INTEGER`]: f16::MAX_EXACT_INTEGER
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/// [`MIN_EXACT_INTEGER`]: f16::MIN_EXACT_INTEGER
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/// ```
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/// #![feature(f16)]
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/// #![feature(float_exact_integer_constants)]
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/// # // FIXME(#152635): Float rounding on `i586` does not adhere to IEEE 754
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/// # #[cfg(not(all(target_arch = "x86", not(target_feature = "sse"))))] {
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/// # #[cfg(target_has_reliable_f16)] {
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/// let min_exact_int = f16::MIN_EXACT_INTEGER;
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/// assert_eq!(min_exact_int, min_exact_int as f16 as i16);
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/// assert_eq!(min_exact_int - 1, (min_exact_int - 1) as f16 as i16);
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/// assert_ne!(min_exact_int - 2, (min_exact_int - 2) as f16 as i16);
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///
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/// // Below `f16::MIN_EXACT_INTEGER`, multiple integers can map to one float value
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/// assert_eq!((min_exact_int - 1) as f16, (min_exact_int - 2) as f16);
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/// # }}
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/// ```
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// #[unstable(feature = "f16", issue = "116909")]
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#[unstable(feature = "float_exact_integer_constants", issue = "152466")]
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pub const MIN_EXACT_INTEGER: i16 = -Self::MAX_EXACT_INTEGER;
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/// The mask of the bit used to encode the sign of an [`f16`].
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///
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/// This bit is set when the sign is negative and unset when the sign is
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/// positive.
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/// If you only need to check whether a value is positive or negative,
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/// [`is_sign_positive`] or [`is_sign_negative`] can be used.
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///
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/// [`is_sign_positive`]: f16::is_sign_positive
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/// [`is_sign_negative`]: f16::is_sign_negative
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/// ```rust
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/// #![feature(float_masks)]
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/// #![feature(f16)]
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/// # #[cfg(target_has_reliable_f16)] {
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/// let sign_mask = f16::SIGN_MASK;
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/// let a = 1.6552f16;
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/// let a_bits = a.to_bits();
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///
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/// assert_eq!(a_bits & sign_mask, 0x0);
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/// assert_eq!(f16::from_bits(a_bits ^ sign_mask), -a);
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/// assert_eq!(sign_mask, (-0.0f16).to_bits());
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/// # }
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/// ```
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#[unstable(feature = "float_masks", issue = "154064")]
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pub const SIGN_MASK: u16 = 0x8000;
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/// The mask of the bits used to encode the exponent of an [`f16`].
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///
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/// Note that the exponent is stored as a biased value, with a bias of 15 for `f16`.
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///
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/// ```rust
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/// #![feature(float_masks)]
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/// #![feature(f16)]
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/// # #[cfg(target_has_reliable_f16)] {
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/// let exponent_mask = f16::EXPONENT_MASK;
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///
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/// fn get_exp(a: f16) -> i16 {
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/// let bias = 15;
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/// let biased = a.to_bits() & f16::EXPONENT_MASK;
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/// (biased >> (f16::MANTISSA_DIGITS - 1)).cast_signed() - bias
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/// }
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///
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/// assert_eq!(get_exp(0.5), -1);
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/// assert_eq!(get_exp(1.0), 0);
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/// assert_eq!(get_exp(2.0), 1);
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/// assert_eq!(get_exp(4.0), 2);
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/// # }
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/// ```
|
||
#[unstable(feature = "float_masks", issue = "154064")]
|
||
pub const EXPONENT_MASK: u16 = 0x7c00;
|
||
|
||
/// The mask of the bits used to encode the mantissa of an [`f16`].
|
||
///
|
||
/// ```rust
|
||
/// #![feature(float_masks)]
|
||
/// #![feature(f16)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
/// let mantissa_mask = f16::MANTISSA_MASK;
|
||
///
|
||
/// assert_eq!(0f16.to_bits() & mantissa_mask, 0x0);
|
||
/// assert_eq!(1f16.to_bits() & mantissa_mask, 0x0);
|
||
///
|
||
/// // multiplying a finite value by a power of 2 doesn't change its mantissa
|
||
/// // unless the result or initial value is not normal.
|
||
/// let a = 1.6552f16;
|
||
/// let b = 4.0 * a;
|
||
/// assert_eq!(a.to_bits() & mantissa_mask, b.to_bits() & mantissa_mask);
|
||
///
|
||
/// // The maximum and minimum values have a saturated significand
|
||
/// assert_eq!(f16::MAX.to_bits() & f16::MANTISSA_MASK, f16::MANTISSA_MASK);
|
||
/// assert_eq!(f16::MIN.to_bits() & f16::MANTISSA_MASK, f16::MANTISSA_MASK);
|
||
/// # }
|
||
/// ```
|
||
#[unstable(feature = "float_masks", issue = "154064")]
|
||
pub const MANTISSA_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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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")]
|
||
#[must_use]
|
||
pub const fn classify(self) -> FpCategory {
|
||
let b = self.to_bits();
|
||
match (b & Self::MANTISSA_MASK, b & Self::EXPONENT_MASK) {
|
||
(0, Self::EXPONENT_MASK) => FpCategory::Infinite,
|
||
(_, Self::EXPONENT_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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// // 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")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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")]
|
||
#[must_use = "method returns a new number and does not mutate the original value"]
|
||
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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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 exactly one of the arguments is NaN (quiet or signaling), then the other argument is
|
||
/// returned. If both arguments are NaN, the return value is NaN, with the bit pattern picked
|
||
/// using the usual [rules for arithmetic operations](f32#nan-bit-patterns). If the inputs
|
||
/// compare equal (such as for the case of `+0.0` and `-0.0`), either input may be returned
|
||
/// non-deterministically.
|
||
///
|
||
/// The handling of NaNs follows the IEEE 754-2019 semantics for `maximumNumber`, treating all
|
||
/// NaNs the same way to ensure the operation is associative. The handling of signed zeros
|
||
/// follows the IEEE 754-2008 semantics for `maxNum`.
|
||
///
|
||
/// ```
|
||
/// #![feature(f16)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// let x = 1.0f16;
|
||
/// let y = 2.0f16;
|
||
///
|
||
/// assert_eq!(x.max(y), y);
|
||
/// assert_eq!(x.max(f16::NAN), 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 max(self, other: f16) -> f16 {
|
||
intrinsics::maximum_number_nsz_f16(self, other)
|
||
}
|
||
|
||
/// Returns the minimum of the two numbers, ignoring NaN.
|
||
///
|
||
/// If exactly one of the arguments is NaN (quiet or signaling), then the other argument is
|
||
/// returned. If both arguments are NaN, the return value is NaN, with the bit pattern picked
|
||
/// using the usual [rules for arithmetic operations](f32#nan-bit-patterns). If the inputs
|
||
/// compare equal (such as for the case of `+0.0` and `-0.0`), either input may be returned
|
||
/// non-deterministically.
|
||
///
|
||
/// The handling of NaNs follows the IEEE 754-2019 semantics for `minimumNumber`, treating all
|
||
/// NaNs the same way to ensure the operation is associative. The handling of signed zeros
|
||
/// follows the IEEE 754-2008 semantics for `minNum`.
|
||
///
|
||
/// ```
|
||
/// #![feature(f16)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// let x = 1.0f16;
|
||
/// let y = 2.0f16;
|
||
///
|
||
/// assert_eq!(x.min(y), x);
|
||
/// assert_eq!(x.min(f16::NAN), 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::minimum_number_nsz_f16(self, other)
|
||
}
|
||
|
||
/// Returns the maximum of the two numbers, propagating NaN.
|
||
///
|
||
/// If at least one of the arguments is NaN, the return value is NaN, with the bit pattern
|
||
/// picked using the usual [rules for arithmetic operations](f32#nan-bit-patterns). Furthermore,
|
||
/// `-0.0` is considered to be less than `+0.0`, making this function fully deterministic for
|
||
/// non-NaN inputs.
|
||
///
|
||
/// This is in contrast to [`f16::max`] which only returns NaN when *both* arguments are NaN,
|
||
/// and which does not reliably order `-0.0` and `+0.0`.
|
||
///
|
||
/// This follows the IEEE 754-2019 semantics for `maximum`.
|
||
///
|
||
/// ```
|
||
/// #![feature(f16)]
|
||
/// #![feature(float_minimum_maximum)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// let x = 1.0f16;
|
||
/// let y = 2.0f16;
|
||
///
|
||
/// assert_eq!(x.maximum(y), y);
|
||
/// assert!(x.maximum(f16::NAN).is_nan());
|
||
/// # }
|
||
/// ```
|
||
#[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.
|
||
///
|
||
/// If at least one of the arguments is NaN, the return value is NaN, with the bit pattern
|
||
/// picked using the usual [rules for arithmetic operations](f32#nan-bit-patterns). Furthermore,
|
||
/// `-0.0` is considered to be less than `+0.0`, making this function fully deterministic for
|
||
/// non-NaN inputs.
|
||
///
|
||
/// This is in contrast to [`f16::min`] which only returns NaN when *both* arguments are NaN,
|
||
/// and which does not reliably order `-0.0` and `+0.0`.
|
||
///
|
||
/// This follows the IEEE 754-2019 semantics for `minimum`.
|
||
///
|
||
/// ```
|
||
/// #![feature(f16)]
|
||
/// #![feature(float_minimum_maximum)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// let x = 1.0f16;
|
||
/// let y = 2.0f16;
|
||
///
|
||
/// assert_eq!(x.minimum(y), x);
|
||
/// assert!(x.minimum(f16::NAN).is_nan());
|
||
/// # }
|
||
/// ```
|
||
#[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_has_reliable_f16)] {
|
||
///
|
||
/// 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")]
|
||
#[must_use = "this returns the result of the operation, \
|
||
without modifying the original"]
|
||
pub const fn midpoint(self, other: f16) -> f16 {
|
||
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 {
|
||
(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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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(target_has_reliable_f16)] {
|
||
///
|
||
/// assert_ne!((1f16).to_bits(), 1f16 as u16); // 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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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(target_has_reliable_f16)] {
|
||
///
|
||
/// 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)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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")]
|
||
#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
|
||
pub const 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. If the result is zero and among the three inputs `self`, `min`, and `max` there are
|
||
/// zeros with different sign, either `0.0` or `-0.0` is returned non-deterministically.
|
||
///
|
||
/// # Panics
|
||
///
|
||
/// Panics if `min > max`, `min` is NaN, or `max` is NaN.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(f16)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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());
|
||
///
|
||
/// // These always returns zero, but the sign (which is ignored by `==`) is non-deterministic.
|
||
/// assert!((0.0f16).clamp(-0.0, -0.0) == 0.0);
|
||
/// assert!((1.0f16).clamp(-0.0, 0.0) == 0.0);
|
||
/// // This is definitely a negative zero.
|
||
/// assert!((-1.0f16).clamp(-0.0, 1.0).is_sign_negative());
|
||
/// # }
|
||
/// ```
|
||
#[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
|
||
}
|
||
|
||
/// Clamps this number to a symmetric range centered around zero.
|
||
///
|
||
/// The method clamps the number's magnitude (absolute value) to be at most `limit`.
|
||
///
|
||
/// This is functionally equivalent to `self.clamp(-limit, limit)`, but is more
|
||
/// explicit about the intent.
|
||
///
|
||
/// # Panics
|
||
///
|
||
/// Panics if `limit` is negative or NaN, as this indicates a logic error.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(f16)]
|
||
/// #![feature(clamp_magnitude)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
/// assert_eq!(5.0f16.clamp_magnitude(3.0), 3.0);
|
||
/// assert_eq!((-5.0f16).clamp_magnitude(3.0), -3.0);
|
||
/// assert_eq!(2.0f16.clamp_magnitude(3.0), 2.0);
|
||
/// assert_eq!((-2.0f16).clamp_magnitude(3.0), -2.0);
|
||
/// # }
|
||
/// ```
|
||
#[inline]
|
||
#[unstable(feature = "clamp_magnitude", issue = "148519")]
|
||
#[must_use = "this returns the clamped value and does not modify the original"]
|
||
pub fn clamp_magnitude(self, limit: f16) -> f16 {
|
||
assert!(limit >= 0.0, "limit must be non-negative");
|
||
let limit = limit.abs(); // Canonicalises -0.0 to 0.0
|
||
self.clamp(-limit, limit)
|
||
}
|
||
|
||
/// Computes the absolute value of `self`.
|
||
///
|
||
/// This function always returns the precise result.
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(f16)]
|
||
/// # #[cfg(target_has_reliable_f16_math)] {
|
||
///
|
||
/// 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 {
|
||
intrinsics::fabs(self)
|
||
}
|
||
|
||
/// Returns a number that represents the sign of `self`.
|
||
///
|
||
/// - `1.0` if the number is positive, `+0.0` or `INFINITY`
|
||
/// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
|
||
/// - NaN if the number is NaN
|
||
///
|
||
/// # Examples
|
||
///
|
||
/// ```
|
||
/// #![feature(f16)]
|
||
/// # #[cfg(target_has_reliable_f16)] {
|
||
///
|
||
/// 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(target_has_reliable_f16_math)] {
|
||
///
|
||
/// 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 {
|
||
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),
|
||
allow(unused_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)] {
|
||
///
|
||
/// 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 {
|
||
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)] {
|
||
///
|
||
/// 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 {
|
||
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)] {
|
||
///
|
||
/// 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 {
|
||
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)] {
|
||
///
|
||
/// 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)] {
|
||
///
|
||
/// 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 {
|
||
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)] {
|
||
///
|
||
/// 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)] {
|
||
///
|
||
/// 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 const fn mul_add(self, a: f16, b: f16) -> f16 {
|
||
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)] {
|
||
///
|
||
/// 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` when
|
||
/// divided by `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)] {
|
||
///
|
||
/// 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.
|
||
///
|
||
/// Note that this function is special in that it can return non-NaN results for NaN inputs. For
|
||
/// example, `f16::powi(f16::NAN, 0)` returns `1.0`. However, if an input is a *signaling*
|
||
/// NaN, then the result is non-deterministically either a NaN or the result that the
|
||
/// corresponding quiet NaN would produce.
|
||
///
|
||
/// # 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)] {
|
||
///
|
||
/// 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);
|
||
/// assert_eq!(f16::powi(0.0, 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 powi(self, n: i32) -> f16 {
|
||
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)] {
|
||
///
|
||
/// 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 {
|
||
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)] {
|
||
///
|
||
/// 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
|
||
}
|
||
}
|