# Primitive Type f16

`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.

## Implementations§

source§### impl f16

### impl f16

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

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

#116909)

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

`f16`

#116909)The radix or base of the internal representation of `f16`

.

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

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

#116909)

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

`f16`

#116909)Number of significant digits in base 2.

source#### pub const DIGITS: u32 = 3u32

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

#116909)

#### pub const DIGITS: u32 = 3u32

`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(log_{10} 2^{MANTISSA_DIGITS − 1}).

source#### pub const EPSILON: f16 = 9.7656E-4f16

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

#116909)

#### pub const EPSILON: f16 = 9.7656E-4f16

`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}.

source#### pub const MIN: f16 = -65504f16

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

#116909)

#### pub const MIN: f16 = -65504f16

`f16`

#116909)Smallest finite `f16`

value.

Equal to −`MAX`

.

source#### pub const MIN_POSITIVE: f16 = 6.1035E-5f16

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

#116909)

#### pub const MIN_POSITIVE: f16 = 6.1035E-5f16

`f16`

#116909)Smallest positive normal `f16`

value.

Equal to 2^{MIN_EXP − 1}.

source#### pub const MAX: f16 = 65504f16

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

#116909)

#### pub const MAX: f16 = 65504f16

`f16`

#116909)Largest finite `f16`

value.

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

source#### pub const MIN_EXP: i32 = -13i32

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

#116909)

#### pub const MIN_EXP: i32 = -13i32

`f16`

#116909)One greater than the minimum possible normal power of 2 exponent.

If *x* = `MIN_EXP`

, then normal numbers
≥ 0.5 × 2^{x}.

source#### pub const MAX_EXP: i32 = 16i32

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

#116909)

#### pub const MAX_EXP: i32 = 16i32

`f16`

#116909)Maximum possible power of 2 exponent.

If *x* = `MAX_EXP`

, then normal numbers
< 1 × 2^{x}.

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

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

#116909)

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

`f16`

#116909)Minimum *x* for which 10^{x} is normal.

Equal to ceil(log_{10} `MIN_POSITIVE`

).

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

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

#116909)

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

`f16`

#116909)Maximum *x* for which 10^{x} is normal.

Equal to floor(log_{10} `MAX`

).

source#### pub const NAN: f16 = NaN_f16

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

#116909)

#### pub const NAN: f16 = NaN_f16

`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). This constant isn’t guaranteed to equal to any specific NaN bitpattern, and the stability of its representation over Rust versions and target platforms isn’t guaranteed.

source#### pub const INFINITY: f16 = +Inf_f16

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

#116909)

#### pub const INFINITY: f16 = +Inf_f16

`f16`

#116909)Infinity (∞).

source#### pub const NEG_INFINITY: f16 = -Inf_f16

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

#116909)

#### pub const NEG_INFINITY: f16 = -Inf_f16

`f16`

#116909)Negative infinity (−∞).

source#### pub const fn is_infinite(self) -> bool

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

#116909)

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

`f16`

#116909)Returns `true`

if this value is positive infinity or negative infinity, and
`false`

otherwise.

source#### pub const fn is_subnormal(self) -> bool

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

#116909)

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

`f16`

#116909)Returns `true`

if the number is subnormal.

```
#![feature(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());
```

source#### pub const fn is_normal(self) -> bool

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

#116909)

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

`f16`

#116909)Returns `true`

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

```
#![feature(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());
```

source#### pub const fn classify(self) -> FpCategory

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

#116909)

#### pub const fn classify(self) -> FpCategory

`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.

source#### pub fn is_sign_positive(self) -> bool

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

#116909)

#### pub fn is_sign_positive(self) -> bool

`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.

source#### pub fn is_sign_negative(self) -> bool

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

#116909)

#### pub fn is_sign_negative(self) -> bool

`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.

source#### pub fn next_up(self) -> Self

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

#116909)

#### pub fn next_up(self) -> Self

`f16`

#116909)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.

source#### pub fn next_down(self) -> Self

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

#116909)

#### pub fn next_down(self) -> Self

`f16`

#116909)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.

source#### pub fn to_degrees(self) -> Self

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

#116909)

#### pub fn to_degrees(self) -> Self

`f16`

#116909)source#### pub fn to_radians(self) -> f16

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

#116909)

#### pub fn to_radians(self) -> f16

`f16`

#116909)source#### pub fn max(self, other: f16) -> f16

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

#116909)

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

`f16`

#116909)Returns the maximum of the two numbers, ignoring NaN.

If one of the arguments is NaN, then the other argument is returned. This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs; this function handles all NaNs the same way and avoids maxNum’s problems with associativity. This also matches the behavior of libm’s fmax.

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

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

#116909)

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

`f16`

#116909)Returns the minimum of the two numbers, ignoring NaN.

If one of the arguments is NaN, then the other argument is returned. This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs; this function handles all NaNs the same way and avoids minNum’s problems with associativity. This also matches the behavior of libm’s fmin.

source#### pub fn maximum(self, other: f16) -> f16

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

#116909)

#### pub fn maximum(self, other: f16) -> f16

`f16`

#116909)Returns the maximum of the two numbers, propagating NaN.

This returns NaN when *either* argument is NaN, as opposed to
`f16::max`

which only returns NaN when *both* arguments are NaN.

```
#![feature(f16)]
#![feature(float_minimum_maximum)]
let x = 1.0f16;
let y = 2.0f16;
assert_eq!(x.maximum(y), y);
assert!(x.maximum(f16::NAN).is_nan());
```

If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater of the two numbers. For this operation, -0.0 is considered to be less than +0.0. Note that this follows the semantics specified in IEEE 754-2019.

Also note that “propagation” of NaNs here doesn’t necessarily mean that the bitpattern of a NaN operand is conserved; see explanation of NaN as a special value for more info.

source#### pub fn minimum(self, other: f16) -> f16

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

#116909)

#### pub fn minimum(self, other: f16) -> f16

`f16`

#116909)Returns the minimum of the two numbers, propagating NaN.

This returns NaN when *either* argument is NaN, as opposed to
`f16::min`

which only returns NaN when *both* arguments are NaN.

```
#![feature(f16)]
#![feature(float_minimum_maximum)]
let x = 1.0f16;
let y = 2.0f16;
assert_eq!(x.minimum(y), x);
assert!(x.minimum(f16::NAN).is_nan());
```

If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser of the two numbers. For this operation, -0.0 is considered to be less than +0.0. Note that this follows the semantics specified in IEEE 754-2019.

Also note that “propagation” of NaNs here doesn’t necessarily mean that the bitpattern of a NaN operand is conserved; see explanation of NaN as a special value for more info.

source#### pub fn midpoint(self, other: f16) -> f16

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

#116909)

#### pub fn midpoint(self, other: f16) -> f16

`f16`

#116909)Calculates the middle point of `self`

and `rhs`

.

This returns NaN when *either* argument is NaN or if a combination of
+inf and -inf is provided as arguments.

##### §Examples

source#### pub unsafe fn to_int_unchecked<Int>(self) -> Intwhere
Self: FloatToInt<Int>,

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

#116909)

#### pub unsafe fn to_int_unchecked<Int>(self) -> Intwhere
Self: FloatToInt<Int>,

`f16`

#116909)Rounds toward zero and converts to any primitive integer type, assuming that the value is finite and fits in that type.

```
#![feature(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

source#### pub const fn to_bits(self) -> u16

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

#116909)

#### pub const fn to_bits(self) -> u16

`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.

source#### pub const fn from_bits(v: u16) -> Self

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

#116909)

#### pub const fn from_bits(v: u16) -> Self

`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.

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

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

#116909)

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

`f16`

#116909)source#### pub const fn to_le_bytes(self) -> [u8; 2]

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

#116909)

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

`f16`

#116909)source#### pub const fn to_ne_bytes(self) -> [u8; 2]

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

#116909)

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

`f16`

#116909)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.

See `from_bits`

for some discussion of the
portability of this operation (there are almost no issues).

##### §Examples

source#### pub const fn from_be_bytes(bytes: [u8; 2]) -> Self

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

#116909)

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

`f16`

#116909)source#### pub const fn from_le_bytes(bytes: [u8; 2]) -> Self

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

#116909)

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

`f16`

#116909)source#### pub const fn from_ne_bytes(bytes: [u8; 2]) -> Self

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

#116909)

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

`f16`

#116909)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.

See `from_bits`

for some discussion of the
portability of this operation (there are almost no issues).

##### §Examples

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

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

#116909)

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

`f16`

#116909)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)]
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()))
}
```

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

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

#116909)

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

`f16`

#116909)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

## Trait Implementations§

1.22.0 · source§### impl AddAssign<&f16> for f16

### impl AddAssign<&f16> for f16

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

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

`+=`

operation. Read more1.8.0 · source§### impl AddAssign for f16

### impl AddAssign for f16

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

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

`+=`

operation. Read more1.22.0 · source§### impl DivAssign<&f16> for f16

### impl DivAssign<&f16> for f16

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

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

`/=`

operation. Read more1.8.0 · source§### impl DivAssign for f16

### impl DivAssign for f16

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

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

`/=`

operation. Read more1.22.0 · source§### impl MulAssign<&f16> for f16

### impl MulAssign<&f16> for f16

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

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

`*=`

operation. Read more1.8.0 · source§### impl MulAssign for f16

### impl MulAssign for f16

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

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

`*=`

operation. Read more1.0.0 · source§### impl PartialOrd for f16

### impl PartialOrd for f16

1.0.0 · source§### impl Rem for f16

### 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

1.22.0 · source§### impl RemAssign<&f16> for f16

### impl RemAssign<&f16> for f16

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

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

`%=`

operation. Read more1.8.0 · source§### impl RemAssign for f16

### impl RemAssign for f16

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

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

`%=`

operation. Read more1.22.0 · source§### impl SubAssign<&f16> for f16

### impl SubAssign<&f16> for f16

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

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

`-=`

operation. Read more1.8.0 · source§### impl SubAssign for f16

### impl SubAssign for f16

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

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

`-=`

operation. Read more