Struct half :: f16 Copy item path

impl f16

pub const fn from_bits(bits: u16) -> f16

Constructs a 16-bit floating point value from the raw bits.

pub fn from_f32(value: f32) -> f16

Constructs a 16-bit floating point value from a 32-bit floating point value.

This operation is lossy. If the 32-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are preserved. 32-bit subnormal values are too tiny to be represented in 16-bits and result in ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals or ±0. All other values are truncated and rounded to the nearest representable 16-bit value.

pub const fn from_f32_const(value: f32) -> f16

Constructs a 16-bit floating point value from a 32-bit floating point value.

This function is identical to from_f32 except it never uses hardware intrinsics, which allows it to be const. from_f32 should be preferred in any non-const context.

This operation is lossy. If the 32-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are preserved. 32-bit subnormal values are too tiny to be represented in 16-bits and result in ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals or ±0. All other values are truncated and rounded to the nearest representable 16-bit value.

pub fn from_f64(value: f64) -> f16

Constructs a 16-bit floating point value from a 64-bit floating point value.

This operation is lossy. If the 64-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are preserved. 64-bit subnormal values are too tiny to be represented in 16-bits and result in ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals or ±0. All other values are truncated and rounded to the nearest representable 16-bit value.

pub const fn from_f64_const(value: f64) -> f16

Constructs a 16-bit floating point value from a 64-bit floating point value.

This function is identical to from_f64 except it never uses hardware intrinsics, which allows it to be const. from_f64 should be preferred in any non-const context.

This operation is lossy. If the 64-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are preserved. 64-bit subnormal values are too tiny to be represented in 16-bits and result in ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals or ±0. All other values are truncated and rounded to the nearest representable 16-bit value.

pub const fn to_bits(self) -> u16

Converts a [f16] into the underlying bit representation.

pub const fn to_le_bytes(self) -> [u8; 2]

Returns the memory representation of the underlying bit representation as a byte array in little-endian byte order.

§Examples

let bytes = f16::from_f32(12.5).to_le_bytes();
assert_eq!(bytes, [0x40, 0x4A]);

pub const fn to_be_bytes(self) -> [u8; 2]

Returns the memory representation of the underlying bit representation as a byte array in big-endian (network) byte order.

§Examples

let bytes = f16::from_f32(12.5).to_be_bytes();
assert_eq!(bytes, [0x4A, 0x40]);

pub const fn to_ne_bytes(self) -> [u8; 2]

Returns the memory representation of the underlying bit representation 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.

§Examples

let bytes = f16::from_f32(12.5).to_ne_bytes();
assert_eq!(bytes, if cfg!(target_endian = "big") {
    [0x4A, 0x40]
} else {
    [0x40, 0x4A]
});

pub const fn from_le_bytes(bytes: [u8; 2]) -> f16

Creates a floating point value from its representation as a byte array in little endian.

§Examples

let value = f16::from_le_bytes([0x40, 0x4A]);
assert_eq!(value, f16::from_f32(12.5));

pub const fn from_be_bytes(bytes: [u8; 2]) -> f16

Creates a floating point value from its representation as a byte array in big endian.

§Examples

let value = f16::from_be_bytes([0x4A, 0x40]);
assert_eq!(value, f16::from_f32(12.5));

pub const fn from_ne_bytes(bytes: [u8; 2]) -> f16

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.

§Examples

let value = f16::from_ne_bytes(if cfg!(target_endian = "big") {
    [0x4A, 0x40]
} else {
    [0x40, 0x4A]
});
assert_eq!(value, f16::from_f32(12.5));

pub fn to_f32(self) -> f32

Converts a [f16] value into a f32 value.

This conversion is lossless as all 16-bit floating point values can be represented exactly in 32-bit floating point.

pub const fn to_f32_const(self) -> f32

Converts a [f16] value into a f32 value.

This function is identical to to_f32 except it never uses hardware intrinsics, which allows it to be const. to_f32 should be preferred in any non-const context.

This conversion is lossless as all 16-bit floating point values can be represented exactly in 32-bit floating point.

pub fn to_f64(self) -> f64

Converts a [f16] value into a f64 value.

This conversion is lossless as all 16-bit floating point values can be represented exactly in 64-bit floating point.

pub const fn to_f64_const(self) -> f64

Converts a [f16] value into a f64 value.

This function is identical to to_f64 except it never uses hardware intrinsics, which allows it to be const. to_f64 should be preferred in any non-const context.

This conversion is lossless as all 16-bit floating point values can be represented exactly in 64-bit floating point.

pub const fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

§Examples


let nan = f16::NAN;
let f = f16::from_f32(7.0_f32);

assert!(nan.is_nan());
assert!(!f.is_nan());

pub const fn is_infinite(self) -> bool

Returns true if this value is ±∞ and false. otherwise.

§Examples


let f = f16::from_f32(7.0f32);
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());

pub const fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

§Examples


let f = f16::from_f32(7.0f32);
let inf = f16::INFINITY;
let neg_inf = f16::NEG_INFINITY;
let nan = f16::NAN;

assert!(f.is_finite());

assert!(!nan.is_finite());
assert!(!inf.is_finite());
assert!(!neg_inf.is_finite());

pub const fn is_normal(self) -> bool

Returns true if the number is neither zero, infinite, subnormal, or NaN.

§Examples


let min = f16::MIN_POSITIVE;
let max = f16::MAX;
let lower_than_min = f16::from_f32(1.0e-10_f32);
let zero = f16::from_f32(0.0_f32);

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());

pub const fn classify(self) -> FpCategory

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.

§Examples

use std::num::FpCategory;

let num = f16::from_f32(12.4_f32);
let inf = f16::INFINITY;

assert_eq!(num.classify(), FpCategory::Normal);
assert_eq!(inf.classify(), FpCategory::Infinite);

pub const fn signum(self) -> f16

Returns a number that represents the sign of self.

1.0 if the number is positive, +0.0 or INFINITY
-1.0 if the number is negative, -0.0 or NEG_INFINITY
NAN if the number is NaN

§Examples


let f = f16::from_f32(3.5_f32);

assert_eq!(f.signum(), f16::from_f32(1.0));
assert_eq!(f16::NEG_INFINITY.signum(), f16::from_f32(-1.0));

assert!(f16::NAN.signum().is_nan());

pub const fn is_sign_positive(self) -> bool

Returns true if and only if self has a positive sign, including +0.0, NaNs with a positive sign bit and +∞.

§Examples


let nan = f16::NAN;
let f = f16::from_f32(7.0_f32);
let g = f16::from_f32(-7.0_f32);

assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());
// `NaN` can be either positive or negative
assert!(nan.is_sign_positive() != nan.is_sign_negative());

pub const fn is_sign_negative(self) -> bool

Returns true if and only if self has a negative sign, including -0.0, NaNs with a negative sign bit and −∞.

§Examples


let nan = f16::NAN;
let f = f16::from_f32(7.0f32);
let g = f16::from_f32(-7.0f32);

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());
// `NaN` can be either positive or negative
assert!(nan.is_sign_positive() != nan.is_sign_negative());

pub const fn copysign(self, sign: f16) -> f16

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 NaN, then NaN with the sign of sign is returned.

§Examples

let f = f16::from_f32(3.5);

assert_eq!(f.copysign(f16::from_f32(0.42)), f16::from_f32(3.5));
assert_eq!(f.copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5));
assert_eq!((-f).copysign(f16::from_f32(0.42)), f16::from_f32(3.5));
assert_eq!((-f).copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5));

assert!(f16::NAN.copysign(f16::from_f32(1.0)).is_nan());

pub fn max(self, other: f16) -> f16

Returns the maximum of the two numbers.

If one of the arguments is NaN, then the other argument is returned.

§Examples

let x = f16::from_f32(1.0);
let y = f16::from_f32(2.0);

assert_eq!(x.max(y), y);

pub fn min(self, other: f16) -> f16

Returns the minimum of the two numbers.

If one of the arguments is NaN, then the other argument is returned.

§Examples

let x = f16::from_f32(1.0);
let y = f16::from_f32(2.0);

assert_eq!(x.min(y), x);

pub fn clamp(self, min: f16, max: f16) -> f16

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

assert!(f16::from_f32(-3.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(-2.0));
assert!(f16::from_f32(0.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(0.0));
assert!(f16::from_f32(2.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(1.0));
assert!(f16::NAN.clamp(f16::from_f32(-2.0), f16::from_f32(1.0)).is_nan());

pub fn total_cmp(&self, other: &Self) -> Ordering

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.

§Examples

let mut v: Vec<f16> = vec![];
v.push(f16::ONE);
v.push(f16::INFINITY);
v.push(f16::NEG_INFINITY);
v.push(f16::NAN);
v.push(f16::MAX_SUBNORMAL);
v.push(-f16::MAX_SUBNORMAL);
v.push(f16::ZERO);
v.push(f16::NEG_ZERO);
v.push(f16::NEG_ONE);
v.push(f16::MIN_POSITIVE);

v.sort_by(|a, b| a.total_cmp(&b));

assert!(v
    .into_iter()
    .zip(
        [
            f16::NEG_INFINITY,
            f16::NEG_ONE,
            -f16::MAX_SUBNORMAL,
            f16::NEG_ZERO,
            f16::ZERO,
            f16::MAX_SUBNORMAL,
            f16::MIN_POSITIVE,
            f16::ONE,
            f16::INFINITY,
            f16::NAN
        ]
        .iter()
    )
    .all(|(a, b)| a.to_bits() == b.to_bits()));

pub const DIGITS: u32 = 3u32

Approximate number of [f16] significant digits in base 10

pub const EPSILON: f16 = _

[f16] machine epsilon value

This is the difference between 1.0 and the next largest representable number.

pub const INFINITY: f16 = _

[f16] positive Infinity (+∞)

pub const MANTISSA_DIGITS: u32 = 11u32

Number of [f16] significant digits in base 2

pub const MAX: f16 = _

Largest finite [f16] value

pub const MAX_10_EXP: i32 = 4i32

Maximum possible [f16] power of 10 exponent

pub const MAX_EXP: i32 = 16i32

Maximum possible [f16] power of 2 exponent

pub const MIN: f16 = _

Smallest finite [f16] value

pub const MIN_10_EXP: i32 = -4i32

Minimum possible normal [f16] power of 10 exponent

pub const MIN_EXP: i32 = -13i32

One greater than the minimum possible normal [f16] power of 2 exponent

pub const MIN_POSITIVE: f16 = _

Smallest positive normal [f16] value

pub const NAN: f16 = _

[f16] Not a Number (NaN)

pub const NEG_INFINITY: f16 = _

[f16] negative infinity (-∞)

pub const RADIX: u32 = 2u32

The radix or base of the internal representation of [f16]

pub const MIN_POSITIVE_SUBNORMAL: f16 = _

Minimum positive subnormal [f16] value

pub const MAX_SUBNORMAL: f16 = _

Maximum subnormal [f16] value

pub const ONE: f16 = _

[f16] 1

pub const ZERO: f16 = _

[f16] 0

pub const NEG_ZERO: f16 = _

[f16] -0

pub const NEG_ONE: f16 = _

[f16] -1

pub const E: f16 = _

[f16] Euler’s number (ℯ)

pub const PI: f16 = _

[f16] Archimedes’ constant (π)

pub const FRAC_1_PI: f16 = _

[f16] 1/π

pub const FRAC_1_SQRT_2: f16 = _

[f16] 1/√2

pub const FRAC_2_PI: f16 = _

[f16] 2/π

pub const FRAC_2_SQRT_PI: f16 = _

[f16] 2/√π

pub const FRAC_PI_2: f16 = _

[f16] π/2

pub const FRAC_PI_3: f16 = _

[f16] π/3

pub const FRAC_PI_4: f16 = _

[f16] π/4

pub const FRAC_PI_6: f16 = _

[f16] π/6

pub const FRAC_PI_8: f16 = _

[f16] π/8

pub const LN_10: f16 = _

[f16] 𝗅𝗇 10

pub const LN_2: f16 = _

[f16] 𝗅𝗇 2

pub const LOG10_E: f16 = _

[f16] 𝗅𝗈𝗀₁₀ℯ

pub const LOG10_2: f16 = _

[f16] 𝗅𝗈𝗀₁₀2

pub const LOG2_E: f16 = _

[f16] 𝗅𝗈𝗀₂ℯ

pub const LOG2_10: f16 = _

[f16] 𝗅𝗈𝗀₂10

pub const SQRT_2: f16 = _

[f16] √2

Trait Implementations§

impl Add<&f16> for &f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, rhs: &f16) -> Self::Output

Performs the + operation. Read more

impl Add<&f16> for f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, rhs: &f16) -> Self::Output

Performs the + operation. Read more

impl Add<f16> for &f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, rhs: f16) -> Self::Output

Performs the + operation. Read more

impl Add for f16

type Output = f16

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation. Read more

impl AddAssign<&f16> for f16

fn add_assign(&mut self, rhs: &f16)

Performs the += operation. Read more

impl AddAssign for f16

fn add_assign(&mut self, rhs: Self)

Performs the += operation. Read more