Primitive Type f16

🔬This is a nightly-only experimental API. (f16 #116909)

A 16-bit floating point type (specifically, the “binary16” type defined in IEEE 754-2008).

This type is very similar to f32 but has decreased precision because it uses half as many bits. Please see [the documentation for f32 or Wikipedia on half-precision values for more information.

Note that most common platforms will not support f16 in hardware without enabling extra target features, with the notable exception of Apple Silicon (also known as M1, M2, etc.) processors. Hardware support on x86-64 requires the avx512fp16 feature, while RISC-V requires Zhf. Usually the fallback implementation will be to use f32 hardware if it exists, and convert between f16 and f32 when performing math.

See also the std::f16::consts module.

Implementations

impl f16

pub const RADIX: u32 = 2u32

🔬This is a nightly-only experimental API. (f16 #116909)

The radix or base of the internal representation of f16.

pub const MANTISSA_DIGITS: u32 = 11u32

🔬This is a nightly-only experimental API. (f16 #116909)

Number of significant digits in base 2.

pub const DIGITS: u32 = 3u32

🔬This is a nightly-only experimental API. (f16 #116909)

Approximate number of significant digits in base 10.

This is the maximum x such that any decimal number with x significant digits can be converted to f16 and back without loss.

Equal to floor(log₁₀ 2^{MANTISSA_DIGITS − 1}).

pub const EPSILON: f16 = {transmute(0x1400): f16}

🔬This is a nightly-only experimental API. (f16 #116909)

Machine epsilon value for f16.

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

Equal to 2^{1 − MANTISSA_DIGITS}.

pub const MIN: f16 = {transmute(0xfbff): f16}

🔬This is a nightly-only experimental API. (f16 #116909)

Smallest finite f16 value.

Equal to −MAX.

pub const MIN_POSITIVE: f16 = {transmute(0x0400): f16}

🔬This is a nightly-only experimental API. (f16 #116909)

Smallest positive normal f16 value.

Equal to 2^{MIN_EXP − 1}.

pub const MAX: f16 = {transmute(0x7bff): f16}

🔬This is a nightly-only experimental API. (f16 #116909)

Largest finite f16 value.

Equal to (1 − 2^{−MANTISSA_DIGITS}) 2^MAX_EXP.

pub const MIN_EXP: i32 = -13i32

🔬This is a nightly-only experimental API. (f16 #116909)

One greater than the minimum possible normal power of 2 exponent.

If x = MIN_EXP, then normal numbers ≥ 0.5 × 2^x.

pub const MAX_EXP: i32 = 16i32

🔬This is a nightly-only experimental API. (f16 #116909)

Maximum possible power of 2 exponent.

If x = MAX_EXP, then normal numbers < 1 × 2^x.

pub const MIN_10_EXP: i32 = -4i32

🔬This is a nightly-only experimental API. (f16 #116909)

Minimum x for which 10^x is normal.

Equal to ceil(log₁₀ MIN_POSITIVE).

pub const MAX_10_EXP: i32 = 4i32

🔬This is a nightly-only experimental API. (f16 #116909)

Maximum x for which 10^x is normal.

Equal to floor(log₁₀ MAX).

pub const fn is_nan(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if this value is NaN.

pub fn is_sign_positive(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

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 result in some cases. See explanation of NaN as a special value for more info.

#![feature(f16)]

let f = 7.0_f16;
let g = -7.0_f16;

assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());

pub fn is_sign_negative(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

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 result in some cases. See explanation of NaN as a special value for more info.

#![feature(f16)]

let f = 7.0_f16;
let g = -7.0_f16;

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());

pub fn to_bits(self) -> u16

🔬This is a nightly-only experimental API. (f16 #116909)

Raw transmutation to u16.

This is currently identical to transmute::<f16, u16>(self) on all platforms.

See 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.

pub fn from_bits(v: u16) -> Self

🔬This is a nightly-only experimental API. (f16 #116909)

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.

Trait Implementations

impl Add<&f16> for &f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, other: &f16) -> <f16 as Add<f16>>::Output

Performs the + operation.

impl Add<&f16> for f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, other: &f16) -> <f16 as Add<f16>>::Output

Performs the + operation.

impl<'a> Add<f16> for &'a f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, other: f16) -> <f16 as Add<f16>>::Output

Performs the + operation.

impl Add for f16

type Output = f16

The resulting type after applying the + operator.

const fn add(self, other: f16) -> f16

Performs the + operation.

impl AddAssign<&f16> for f16

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

Performs the += operation.

impl AddAssign for f16

fn add_assign(&mut self, other: f16)

Performs the += operation.

impl Clone for f16

fn clone(&self) -> Self

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for f16

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for f16

fn default() -> f16

Returns the default value of 0.0

impl Div<&f16> for &f16

type Output = <f16 as Div>::Output

The resulting type after applying the / operator.

fn div(self, other: &f16) -> <f16 as Div<f16>>::Output

Performs the / operation.

impl Div<&f16> for f16

type Output = <f16 as Div>::Output

The resulting type after applying the / operator.

fn div(self, other: &f16) -> <f16 as Div<f16>>::Output

Performs the / operation.

impl<'a> Div<f16> for &'a f16

type Output = <f16 as Div>::Output

The resulting type after applying the / operator.

fn div(self, other: f16) -> <f16 as Div<f16>>::Output

Performs the / operation.

impl Div for f16

type Output = f16

The resulting type after applying the / operator.

fn div(self, other: f16) -> f16

Performs the / operation.

impl DivAssign<&f16> for f16

fn div_assign(&mut self, other: &f16)

Performs the /= operation.

impl DivAssign for f16

fn div_assign(&mut self, other: f16)

Performs the /= operation.

impl From<f16> for f128

fn from(small: f16) -> Self

Converts f16 to f128 losslessly.

impl From<f16> for f64

fn from(small: f16) -> Self

Converts f16 to f64 losslessly.

impl Mul<&f16> for &f16

type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, other: &f16) -> <f16 as Mul<f16>>::Output

Performs the * operation.

impl Mul<&f16> for f16

type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, other: &f16) -> <f16 as Mul<f16>>::Output

Performs the * operation.

impl<'a> Mul<f16> for &'a f16

type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, other: f16) -> <f16 as Mul<f16>>::Output

Performs the * operation.

impl Mul for f16

type Output = f16

The resulting type after applying the * operator.

fn mul(self, other: f16) -> f16

Performs the * operation.

impl MulAssign<&f16> for f16

fn mul_assign(&mut self, other: &f16)

Performs the *= operation.

impl MulAssign for f16

fn mul_assign(&mut self, other: f16)

Performs the *= operation.

impl Neg for &f16

type Output = <f16 as Neg>::Output

The resulting type after applying the - operator.

fn neg(self) -> <f16 as Neg>::Output

Performs the unary - operation.

impl Neg for f16

type Output = f16

The resulting type after applying the - operator.

fn neg(self) -> f16

Performs the unary - operation.

impl PartialEq for f16

const fn eq(&self, other: &f16) -> bool

This method tests for self and other values to be equal, and is used by ==.

const fn ne(&self, other: &f16) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for f16

fn partial_cmp(&self, other: &f16) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &f16) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &f16) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn ge(&self, other: &f16) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

fn gt(&self, other: &f16) -> bool

This method tests greater than (for self and other) and is used by the > operator.

impl Rem<&f16> for &f16

type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, other: &f16) -> <f16 as Rem<f16>>::Output

Performs the % operation.

impl Rem<&f16> for f16

type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, other: &f16) -> <f16 as Rem<f16>>::Output

Performs the % operation.

impl<'a> Rem<f16> for &'a f16

type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, other: f16) -> <f16 as Rem<f16>>::Output

Performs the % operation.

impl Rem for f16

The remainder from the division of two floats.

The remainder has the same sign as the dividend and is computed as: x - (x / y).trunc() * y.

Examples

let x: f32 = 50.50;
let y: f32 = 8.125;
let remainder = x - (x / y).trunc() * y;

// The answer to both operations is 1.75
assert_eq!(x % y, remainder);

type Output = f16

The resulting type after applying the % operator.

fn rem(self, other: f16) -> f16

Performs the % operation.

impl RemAssign<&f16> for f16

fn rem_assign(&mut self, other: &f16)

Performs the %= operation.

impl RemAssign for f16

fn rem_assign(&mut self, other: f16)

Performs the %= operation.

impl Sub<&f16> for &f16

type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, other: &f16) -> <f16 as Sub<f16>>::Output

Performs the - operation.

impl Sub<&f16> for f16

type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, other: &f16) -> <f16 as Sub<f16>>::Output

Performs the - operation.

impl<'a> Sub<f16> for &'a f16

type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, other: f16) -> <f16 as Sub<f16>>::Output

Performs the - operation.

impl Sub for f16

type Output = f16

The resulting type after applying the - operator.

fn sub(self, other: f16) -> f16

Performs the - operation.

impl SubAssign<&f16> for f16

fn sub_assign(&mut self, other: &f16)

Performs the -= operation.

impl SubAssign for f16

fn sub_assign(&mut self, other: f16)

Performs the -= operation.

impl Copy for f16

impl FloatToInt<i128> for f16

impl FloatToInt<i16> for f16

impl FloatToInt<i32> for f16

impl FloatToInt<i64> for f16

impl FloatToInt<i8> for f16

impl FloatToInt<isize> for f16

impl FloatToInt<u128> for f16

impl FloatToInt<u16> for f16

impl FloatToInt<u32> for f16

impl FloatToInt<u64> for f16

impl FloatToInt<u8> for f16

impl FloatToInt<usize> for f16