# Primitive Type f16

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

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§

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### impl f16

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#### pub const RADIX: u32 = 2u32

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

The radix or base of the internal representation of `f16`.

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#### pub const MANTISSA_DIGITS: u32 = 11u32

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

Number of significant digits in base 2.

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#### 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).

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#### 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 21 − `MANTISSA_DIGITS`.

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

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

Smallest finite `f16` value.

Equal to −`MAX`.

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#### 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.

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#### 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`.

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#### 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 × 2x.

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#### 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 × 2x.

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#### pub const MIN_10_EXP: i32 = -4i32

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

Minimum x for which 10x is normal.

Equal to ceil(log10 `MIN_POSITIVE`).

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#### pub const MAX_10_EXP: i32 = 4i32

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

Maximum x for which 10x is normal.

Equal to floor(log10 `MAX`).

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#### pub const fn is_nan(self) -> bool

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

Returns `true` if this value is NaN.

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#### 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());

Run
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#### 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());

Run
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#### 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.

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#### 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§

1.0.0 · source§

### impl Add<&f16> for &f16

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#### type Output = <f16 as Add>::Output

The resulting type after applying the `+` operator.
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#### fn add(self, other: &f16) -> <f16 as Add<f16>>::Output

Performs the `+` operation. Read more
1.0.0 · source§

### impl Add<&f16> for f16

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#### type Output = <f16 as Add>::Output

The resulting type after applying the `+` operator.
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#### fn add(self, other: &f16) -> <f16 as Add<f16>>::Output

Performs the `+` operation. Read more
1.0.0 · source§

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

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#### type Output = <f16 as Add>::Output

The resulting type after applying the `+` operator.
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#### fn add(self, other: f16) -> <f16 as Add<f16>>::Output

Performs the `+` operation. Read more
1.0.0 (const: unstable) · source§

### impl Add for f16

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#### type Output = f16

The resulting type after applying the `+` operator.
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#### const fn add(self, other: f16) -> f16

Performs the `+` operation. Read more
1.22.0 · source§

### impl AddAssign<&f16> for f16

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

Performs the `+=` operation. Read more
1.8.0 · source§

### impl AddAssign for f16

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

Performs the `+=` operation. Read more
1.0.0 · source§

### impl Clone for f16

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#### fn clone(&self) -> Self

Returns a copy of the value. Read more
1.0.0 · source§

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

Performs copy-assignment from `source`. Read more
1.0.0 · source§

### impl Debug for f16

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

Formats the value using the given formatter. Read more
1.0.0 · source§

### impl Default for f16

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#### fn default() -> f16

Returns the default value of `0.0`

1.0.0 · source§

### impl Div<&f16> for &f16

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#### type Output = <f16 as Div>::Output

The resulting type after applying the `/` operator.
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#### fn div(self, other: &f16) -> <f16 as Div<f16>>::Output

Performs the `/` operation. Read more
1.0.0 · source§

### impl Div<&f16> for f16

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#### type Output = <f16 as Div>::Output

The resulting type after applying the `/` operator.
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#### fn div(self, other: &f16) -> <f16 as Div<f16>>::Output

Performs the `/` operation. Read more
1.0.0 · source§

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

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#### type Output = <f16 as Div>::Output

The resulting type after applying the `/` operator.
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#### fn div(self, other: f16) -> <f16 as Div<f16>>::Output

Performs the `/` operation. Read more
1.0.0 · source§

### impl Div for f16

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#### type Output = f16

The resulting type after applying the `/` operator.
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#### fn div(self, other: f16) -> f16

Performs the `/` operation. Read more
1.22.0 · source§

### impl DivAssign<&f16> for f16

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

Performs the `/=` operation. Read more
1.8.0 · source§

### impl DivAssign for f16

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

Performs the `/=` operation. Read more
1.6.0 · source§

### impl From<f16> for f128

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#### fn from(small: f16) -> Self

Converts `f16` to `f128` losslessly.

1.6.0 · source§

### impl From<f16> for f64

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#### fn from(small: f16) -> Self

Converts `f16` to `f64` losslessly.

1.0.0 · source§

### impl Mul<&f16> for &f16

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#### type Output = <f16 as Mul>::Output

The resulting type after applying the `*` operator.
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#### fn mul(self, other: &f16) -> <f16 as Mul<f16>>::Output

Performs the `*` operation. Read more
1.0.0 · source§

### impl Mul<&f16> for f16

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#### type Output = <f16 as Mul>::Output

The resulting type after applying the `*` operator.
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#### fn mul(self, other: &f16) -> <f16 as Mul<f16>>::Output

Performs the `*` operation. Read more
1.0.0 · source§

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

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#### type Output = <f16 as Mul>::Output

The resulting type after applying the `*` operator.
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#### fn mul(self, other: f16) -> <f16 as Mul<f16>>::Output

Performs the `*` operation. Read more
1.0.0 · source§

### impl Mul for f16

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#### type Output = f16

The resulting type after applying the `*` operator.
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#### fn mul(self, other: f16) -> f16

Performs the `*` operation. Read more
1.22.0 · source§

### impl MulAssign<&f16> for f16

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

Performs the `*=` operation. Read more
1.8.0 · source§

### impl MulAssign for f16

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

Performs the `*=` operation. Read more
1.0.0 · source§

### impl Neg for &f16

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#### type Output = <f16 as Neg>::Output

The resulting type after applying the `-` operator.
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#### fn neg(self) -> <f16 as Neg>::Output

Performs the unary `-` operation. Read more
1.0.0 · source§

### impl Neg for f16

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#### type Output = f16

The resulting type after applying the `-` operator.
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#### fn neg(self) -> f16

Performs the unary `-` operation. Read more
1.0.0 (const: unstable) · source§

### impl PartialEq for f16

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

This method tests for `self` and `other` values to be equal, and is used by `==`.
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#### 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.
1.0.0 · source§

### impl PartialOrd for f16

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

This method returns an ordering between `self` and `other` values if one exists. Read more
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#### fn lt(&self, other: &f16) -> bool

This method tests less than (for `self` and `other`) and is used by the `<` operator. Read more
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#### fn le(&self, other: &f16) -> bool

This method tests less than or equal to (for `self` and `other`) and is used by the `<=` operator. Read more
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#### fn ge(&self, other: &f16) -> bool

This method tests greater than or equal to (for `self` and `other`) and is used by the `>=` operator. Read more
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#### fn gt(&self, other: &f16) -> bool

This method tests greater than (for `self` and `other`) and is used by the `>` operator. Read more
1.0.0 · source§

### impl Rem<&f16> for &f16

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#### type Output = <f16 as Rem>::Output

The resulting type after applying the `%` operator.
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#### fn rem(self, other: &f16) -> <f16 as Rem<f16>>::Output

Performs the `%` operation. Read more
1.0.0 · source§

### impl Rem<&f16> for f16

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#### type Output = <f16 as Rem>::Output

The resulting type after applying the `%` operator.
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#### fn rem(self, other: &f16) -> <f16 as Rem<f16>>::Output

Performs the `%` operation. Read more
1.0.0 · source§

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

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#### type Output = <f16 as Rem>::Output

The resulting type after applying the `%` operator.
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#### fn rem(self, other: f16) -> <f16 as Rem<f16>>::Output

Performs the `%` operation. Read more
1.0.0 · source§

### 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);

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#### type Output = f16

The resulting type after applying the `%` operator.
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#### fn rem(self, other: f16) -> f16

Performs the `%` operation. Read more
1.22.0 · source§

### impl RemAssign<&f16> for f16

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

Performs the `%=` operation. Read more
1.8.0 · source§

### impl RemAssign for f16

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

Performs the `%=` operation. Read more
1.0.0 · source§

### impl Sub<&f16> for &f16

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#### type Output = <f16 as Sub>::Output

The resulting type after applying the `-` operator.
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#### fn sub(self, other: &f16) -> <f16 as Sub<f16>>::Output

Performs the `-` operation. Read more
1.0.0 · source§

### impl Sub<&f16> for f16

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#### type Output = <f16 as Sub>::Output

The resulting type after applying the `-` operator.
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#### fn sub(self, other: &f16) -> <f16 as Sub<f16>>::Output

Performs the `-` operation. Read more
1.0.0 · source§

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

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#### type Output = <f16 as Sub>::Output

The resulting type after applying the `-` operator.
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#### fn sub(self, other: f16) -> <f16 as Sub<f16>>::Output

Performs the `-` operation. Read more
1.0.0 · source§

### impl Sub for f16

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#### type Output = f16

The resulting type after applying the `-` operator.
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#### fn sub(self, other: f16) -> f16

Performs the `-` operation. Read more
1.22.0 · source§

### impl SubAssign<&f16> for f16

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

Performs the `-=` operation. Read more
1.8.0 · source§

### impl SubAssign for f16

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

Performs the `-=` operation. Read more
1.0.0 · source§

### impl Copy for f16

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### impl FloatToInt<i128> for f16

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### impl FloatToInt<i16> for f16

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### impl FloatToInt<i32> for f16

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### impl FloatToInt<i64> for f16

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### impl FloatToInt<i8> for f16

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### impl FloatToInt<isize> for f16

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### impl FloatToInt<u128> for f16

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### impl FloatToInt<u16> for f16

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### impl FloatToInt<u32> for f16

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### impl FloatToInt<u64> for f16

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### impl FloatToInt<u8> for f16

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### impl FloatToInt<usize> for f16

## Auto Trait Implementations§

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### impl Freeze for f16

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### impl RefUnwindSafe for f16

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### impl Send for f16

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### impl Sync for f16

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### impl Unpin for f16

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### impl UnwindSafe for f16

## Blanket Implementations§

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### impl<T> Any for T
where T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
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### impl<T> Borrow<T> for T
where T: ?Sized,

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#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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### impl<T> BorrowMut<T> for T
where T: ?Sized,

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#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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### impl<T> From<T> for T

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#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for T
where U: From<T>,

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#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

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### impl<T, U> TryFrom<U> for T
where U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
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#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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### impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.