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
Sourcepub 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
.
Sourcepub 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.
Sourcepub 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(log10 2MANTISSA_DIGITS
− 1).
Sourcepub 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 21 − MANTISSA_DIGITS
.
Sourcepub 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
.
Sourcepub 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 2MIN_EXP
− 1.
Sourcepub 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
) 2MAX_EXP
.
Sourcepub 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 × 2x.
Sourcepub 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 × 2x.
Sourcepub 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 10x is normal.
Equal to ceil(log10 MIN_POSITIVE
).
Sourcepub 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 10x is normal.
Equal to floor(log10 MAX
).
Sourcepub 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.
Sourcepub const INFINITY: f16 = +Inf_f16
🔬This is a nightly-only experimental API. (f16
#116909)
pub const INFINITY: f16 = +Inf_f16
f16
#116909)Infinity (∞).
Sourcepub 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 (−∞).
Sourcepub 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.
Sourcepub 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());
Sourcepub 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());
Sourcepub 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.
Sourcepub const fn is_sign_positive(self) -> bool
🔬This is a nightly-only experimental API. (f16
#116909)
pub const 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 or non-portable result. See the specification
of NaN bit patterns for more info. Use self.signum() == 1.0
if you need fully portable behavior (will return false
for all NaNs).
Sourcepub const fn is_sign_negative(self) -> bool
🔬This is a nightly-only experimental API. (f16
#116909)
pub const 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 or non-portable result. See the specification
of NaN bit patterns for more info. Use self.signum() == -1.0
if you need fully portable behavior (will return false
for all NaNs).
Sourcepub const fn next_up(self) -> Self
🔬This is a nightly-only experimental API. (f16
#116909)
pub const 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 returnsself
; - if
self
isNEG_INFINITY
, this returnsMIN
; - if
self
is-TINY
, this returns -0.0; - if
self
is -0.0 or +0.0, this returnsTINY
; - if
self
isMAX
orINFINITY
, this returnsINFINITY
; - 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.
Sourcepub const fn next_down(self) -> Self
🔬This is a nightly-only experimental API. (f16
#116909)
pub const 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 returnsself
; - if
self
isINFINITY
, this returnsMAX
; - if
self
isTINY
, this returns 0.0; - if
self
is -0.0 or +0.0, this returns-TINY
; - if
self
isMIN
orNEG_INFINITY
, this returnsNEG_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.
Sourcepub const fn to_degrees(self) -> Self
🔬This is a nightly-only experimental API. (f16
#116909)
pub const fn to_degrees(self) -> Self
f16
#116909)Sourcepub const fn to_radians(self) -> f16
🔬This is a nightly-only experimental API. (f16
#116909)
pub const fn to_radians(self) -> f16
f16
#116909)Sourcepub const fn max(self, other: f16) -> f16
🔬This is a nightly-only experimental API. (f16
#116909)
pub const 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.
Sourcepub const fn min(self, other: f16) -> f16
🔬This is a nightly-only experimental API. (f16
#116909)
pub const 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.
Sourcepub const fn maximum(self, other: f16) -> f16
🔬This is a nightly-only experimental API. (f16
#116909)
pub const 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 the specification of NaN bit patterns for more info.
Sourcepub const fn minimum(self, other: f16) -> f16
🔬This is a nightly-only experimental API. (f16
#116909)
pub const 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 the specification of NaN bit patterns for more info.
Sourcepub 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
Sourcepub 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
Sourcepub 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.
Sourcepub 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.
Sourcepub 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)Sourcepub 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)Sourcepub 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
Sourcepub 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)Sourcepub 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)Sourcepub 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
Sourcepub 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()))
}
Sourcepub const fn clamp(self, min: f16, max: f16) -> f16
🔬This is a nightly-only experimental API. (f16
#116909)
pub const 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