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/x86-64 requires the avx512fp16 or avx10.1 features, while RISC-V requires Zfh, and Arm/AArch64 requires FEAT_FP16. 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 = 2

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

The radix or base of the internal representation of f16.

pub const MANTISSA_DIGITS: u32 = 11

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

Number of significant digits in base 2.

Note that the size of the mantissa in the bitwise representation is one smaller than this since the leading 1 is not stored explicitly.

pub const DIGITS: u32 = 3

🔬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 = 9.7656e-4_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 = -6.5504e+4_f16

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

Smallest finite f16 value.

Equal to −MAX.

pub const MIN_POSITIVE: f16 = 6.1035e-5_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 = 6.5504e+4_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 = -13

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

One greater than the minimum possible normal power of 2 exponent for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).

This corresponds to the exact minimum possible normal power of 2 exponent for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition). In other words, all normal numbers representable by this type are greater than or equal to 0.5 × 2^MIN_EXP.

pub const MAX_EXP: i32 = 16

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

One greater than the maximum possible power of 2 exponent for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).

This corresponds to the exact maximum possible power of 2 exponent for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition). In other words, all numbers representable by this type are strictly less than 2^MAX_EXP.

pub const MIN_10_EXP: i32 = -4

🔬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 = 4

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

Maximum x for which 10^x is normal.

Equal to floor(log₁₀ MAX).

pub const NAN: f16

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

Not a Number (NaN).

Note that IEEE 754 doesn’t define just a single NaN value; a plethora of bit patterns are considered to be NaN. Furthermore, the standard makes a difference between a “signaling” and a “quiet” NaN, and allows inspecting its “payload” (the unspecified bits in the bit pattern) and its sign. See the specification of NaN bit patterns for more info.

This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary. The concrete bit pattern may change across Rust versions and target platforms.

pub const INFINITY: f16

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

Infinity (∞).

pub const NEG_INFINITY: f16

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

Negative infinity (−∞).

pub const fn classify(self) -> FpCategory

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

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)]

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);

pub const 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.

#![feature(f16)]

assert_ne!((1f16).to_bits(), 1f16 as u16); // to_bits() is not casting!
assert_eq!((12.5f16).to_bits(), 0x4a40);

pub const 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.

#![feature(f16)]

let v = f16::from_bits(0x4a40);
assert_eq!(v, 12.5);

pub const fn abs(self) -> Self

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

Computes the absolute value of self.

This function always returns the precise result.

Examples

#![feature(f16)]

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());

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 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 for f16

type Output = f16

The resulting type after applying the + operator.

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 duplicate of the value.

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

where Self:,

Performs copy-assignment from source.

impl Debug for f16

fn fmt(&self, fmt: &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 Display for f16

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

Formats the value using the given formatter.

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 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 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 LowerExp for f16

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

Formats the value using the given formatter.

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 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 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

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

Tests for self and other values to be equal, and is used by ==.

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

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: &Self) -> Option<Ordering>

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

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

Tests less than (for self and other) and is used by the < operator.

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

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

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (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 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 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 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 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<'a> Sum<&'a f16> for f16

fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl Sum for f16

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl UpperExp for f16

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

Formats the value using the given formatter.

impl Copy for f16