Struct half::bf16

#[repr(transparent)]
pub struct bf16(_);

A 16-bit floating point type implementing the bfloat16 format.

The bfloat16 floating point format is a truncated 16-bit version of the IEEE 754 standard binary32, a.k.a f32. bf16 has approximately the same dynamic range as f32 by having a lower precision than f16. While f16 has a precision of 11 bits, bf16 has a precision of only 8 bits.

Like f16, bf16 does not offer arithmetic operations as it is intended for compact storage rather than calculations. Operations should be performed with f32 or higher-precision types and converted to/from bf16 as necessary.

Implementations

impl bf16

pub const fn from_bits(bits: u16) -> bf16

Constructs a bf16 value from the raw bits.

pub fn from_f32(value: f32) -> bf16

Constructs a bf16 value from a 32-bit floating point value.

If the 32-bit value is too large to fit, ±∞ will result. NaN values are preserved. Subnormal values that are too tiny to be represented will result in ±0. All other values are truncated and rounded to the nearest representable value.

pub const fn from_f32_const(value: f32) -> bf16

Constructs a bf16 value from a 32-bit floating point value.

This function is identical to from_f32 except it never uses hardware intrinsics, which allows it to be const. from_f32 should be preferred in any non-const context.

If the 32-bit value is too large to fit, ±∞ will result. NaN values are preserved. Subnormal values that are too tiny to be represented will result in ±0. All other values are truncated and rounded to the nearest representable value.

pub fn from_f64(value: f64) -> bf16

Constructs a bf16 value from a 64-bit floating point value.

If the 64-bit value is to large to fit, ±∞ will result. NaN values are preserved. 64-bit subnormal values are too tiny to be represented and result in ±0. Exponents that underflow the minimum exponent will result in subnormals or ±0. All other values are truncated and rounded to the nearest representable value.

pub const fn from_f64_const(value: f64) -> bf16

Constructs a bf16 value from a 64-bit floating point value.

This function is identical to from_f64 except it never uses hardware intrinsics, which allows it to be const. from_f64 should be preferred in any non-const context.

If the 64-bit value is to large to fit, ±∞ will result. NaN values are preserved. 64-bit subnormal values are too tiny to be represented and result in ±0. Exponents that underflow the minimum exponent will result in subnormals or ±0. All other values are truncated and rounded to the nearest representable value.

pub const fn to_bits(self) -> u16

Converts a bf16 into the underlying bit representation.

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

Returns the memory representation of the underlying bit representation as a byte array in little-endian byte order.

Examples

let bytes = bf16::from_f32(12.5).to_le_bytes();
assert_eq!(bytes, [0x48, 0x41]);

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

Returns the memory representation of the underlying bit representation as a byte array in big-endian (network) byte order.

Examples

let bytes = bf16::from_f32(12.5).to_be_bytes();
assert_eq!(bytes, [0x41, 0x48]);

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

Returns the memory representation of the underlying bit representation 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.

Examples

let bytes = bf16::from_f32(12.5).to_ne_bytes();
assert_eq!(bytes, if cfg!(target_endian = "big") {
    [0x41, 0x48]
} else {
    [0x48, 0x41]
});

pub const fn from_le_bytes(bytes: [u8; 2]) -> bf16

Creates a floating point value from its representation as a byte array in little endian.

Examples

let value = bf16::from_le_bytes([0x48, 0x41]);
assert_eq!(value, bf16::from_f32(12.5));

pub const fn from_be_bytes(bytes: [u8; 2]) -> bf16

Creates a floating point value from its representation as a byte array in big endian.

Examples

let value = bf16::from_be_bytes([0x41, 0x48]);
assert_eq!(value, bf16::from_f32(12.5));

pub const fn from_ne_bytes(bytes: [u8; 2]) -> bf16

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.

Examples

let value = bf16::from_ne_bytes(if cfg!(target_endian = "big") {
    [0x41, 0x48]
} else {
    [0x48, 0x41]
});
assert_eq!(value, bf16::from_f32(12.5));

pub fn to_f32(self) -> f32

Converts a bf16 value into an f32 value.

This conversion is lossless as all values can be represented exactly in f32.

pub const fn to_f32_const(self) -> f32

Converts a bf16 value into an f32 value.

This function is identical to to_f32 except it never uses hardware intrinsics, which allows it to be const. to_f32 should be preferred in any non-const context.

This conversion is lossless as all values can be represented exactly in f32.

pub fn to_f64(self) -> f64

Converts a bf16 value into an f64 value.

This conversion is lossless as all values can be represented exactly in f64.

pub const fn to_f64_const(self) -> f64

Converts a bf16 value into an f64 value.

This function is identical to to_f64 except it never uses hardware intrinsics, which allows it to be const. to_f64 should be preferred in any non-const context.

This conversion is lossless as all values can be represented exactly in f64.

pub const fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

Examples

let nan = bf16::NAN;
let f = bf16::from_f32(7.0_f32);

assert!(nan.is_nan());
assert!(!f.is_nan());

pub const fn is_infinite(self) -> bool

Returns true if this value is ±∞ and false otherwise.

Examples

let f = bf16::from_f32(7.0f32);
let inf = bf16::INFINITY;
let neg_inf = bf16::NEG_INFINITY;
let nan = bf16::NAN;

assert!(!f.is_infinite());
assert!(!nan.is_infinite());

assert!(inf.is_infinite());
assert!(neg_inf.is_infinite());

pub const fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

Examples

let f = bf16::from_f32(7.0f32);
let inf = bf16::INFINITY;
let neg_inf = bf16::NEG_INFINITY;
let nan = bf16::NAN;

assert!(f.is_finite());

assert!(!nan.is_finite());
assert!(!inf.is_finite());
assert!(!neg_inf.is_finite());

pub const fn is_normal(self) -> bool

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

Examples

let min = bf16::MIN_POSITIVE;
let max = bf16::MAX;
let lower_than_min = bf16::from_f32(1.0e-39_f32);
let zero = bf16::from_f32(0.0_f32);

assert!(min.is_normal());
assert!(max.is_normal());

assert!(!zero.is_normal());
assert!(!bf16::NAN.is_normal());
assert!(!bf16::INFINITY.is_normal());
// Values between 0 and `min` are subnormal.
assert!(!lower_than_min.is_normal());

pub const fn classify(self) -> FpCategory

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.

Examples

use std::num::FpCategory;

let num = bf16::from_f32(12.4_f32);
let inf = bf16::INFINITY;

assert_eq!(num.classify(), FpCategory::Normal);
assert_eq!(inf.classify(), FpCategory::Infinite);

pub const fn signum(self) -> bf16

Returns a number that represents the sign of self.

• 1.0 if the number is positive, +0.0 or INFINITY
• −1.0 if the number is negative, −0.0 or [NEG_INFINITY`]bf16::NEG_INFINITY
• NAN if the number is NaN

Examples

let f = bf16::from_f32(3.5_f32);

assert_eq!(f.signum(), bf16::from_f32(1.0));
assert_eq!(bf16::NEG_INFINITY.signum(), bf16::from_f32(-1.0));

assert!(bf16::NAN.signum().is_nan());

pub const fn is_sign_positive(self) -> bool

Returns true if and only if self has a positive sign, including +0.0, NaNs with a positive sign bit and +∞.

Examples

let nan = bf16::NAN;
let f = bf16::from_f32(7.0_f32);
let g = bf16::from_f32(-7.0_f32);

assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());
// NaN can be either positive or negative
assert!(nan.is_sign_positive() != nan.is_sign_negative());

pub const fn is_sign_negative(self) -> bool

Returns true if and only if self has a negative sign, including −0.0, NaNs with a negative sign bit and −∞.

Examples

let nan = bf16::NAN;
let f = bf16::from_f32(7.0f32);
let g = bf16::from_f32(-7.0f32);

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());
// NaN can be either positive or negative
assert!(nan.is_sign_positive() != nan.is_sign_negative());

pub const fn copysign(self, sign: bf16) -> bf16

Returns a number composed of the magnitude of self and the sign of sign.

Equal to self if the sign of self and sign are the same, otherwise equal to -self. If self is NaN, then NaN with the sign of sign is returned.

Examples

let f = bf16::from_f32(3.5);

assert_eq!(f.copysign(bf16::from_f32(0.42)), bf16::from_f32(3.5));
assert_eq!(f.copysign(bf16::from_f32(-0.42)), bf16::from_f32(-3.5));
assert_eq!((-f).copysign(bf16::from_f32(0.42)), bf16::from_f32(3.5));
assert_eq!((-f).copysign(bf16::from_f32(-0.42)), bf16::from_f32(-3.5));

assert!(bf16::NAN.copysign(bf16::from_f32(1.0)).is_nan());

pub fn max(self, other: bf16) -> bf16

Returns the maximum of the two numbers.

If one of the arguments is NaN, then the other argument is returned.

Examples

let x = bf16::from_f32(1.0);
let y = bf16::from_f32(2.0);

assert_eq!(x.max(y), y);

pub fn min(self, other: bf16) -> bf16

Returns the minimum of the two numbers.

If one of the arguments is NaN, then the other argument is returned.

Examples

let x = bf16::from_f32(1.0);
let y = bf16::from_f32(2.0);

assert_eq!(x.min(y), x);

pub fn clamp(self, min: bf16, max: bf16) -> bf16

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

assert!(bf16::from_f32(-3.0).clamp(bf16::from_f32(-2.0), bf16::from_f32(1.0)) == bf16::from_f32(-2.0));
assert!(bf16::from_f32(0.0).clamp(bf16::from_f32(-2.0), bf16::from_f32(1.0)) == bf16::from_f32(0.0));
assert!(bf16::from_f32(2.0).clamp(bf16::from_f32(-2.0), bf16::from_f32(1.0)) == bf16::from_f32(1.0));
assert!(bf16::NAN.clamp(bf16::from_f32(-2.0), bf16::from_f32(1.0)).is_nan());

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

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 bf16. 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.

Examples

let mut v: Vec<bf16> = vec![];
v.push(bf16::ONE);
v.push(bf16::INFINITY);
v.push(bf16::NEG_INFINITY);
v.push(bf16::NAN);
v.push(bf16::MAX_SUBNORMAL);
v.push(-bf16::MAX_SUBNORMAL);
v.push(bf16::ZERO);
v.push(bf16::NEG_ZERO);
v.push(bf16::NEG_ONE);
v.push(bf16::MIN_POSITIVE);

v.sort_by(|a, b| a.total_cmp(&b));

assert!(v
    .into_iter()
    .zip(
        [
            bf16::NEG_INFINITY,
            bf16::NEG_ONE,
            -bf16::MAX_SUBNORMAL,
            bf16::NEG_ZERO,
            bf16::ZERO,
            bf16::MAX_SUBNORMAL,
            bf16::MIN_POSITIVE,
            bf16::ONE,
            bf16::INFINITY,
            bf16::NAN
        ]
        .iter()
    )
    .all(|(a, b)| a.to_bits() == b.to_bits()));

pub const DIGITS: u32 = 2u32

Approximate number of bf16 significant digits in base 10

pub const EPSILON: bf16 = _

bf16 machine epsilon value

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

pub const INFINITY: bf16 = _

bf16 positive Infinity (+∞)

pub const MANTISSA_DIGITS: u32 = 8u32

Number of bf16 significant digits in base 2

pub const MAX: bf16 = _

Largest finite bf16 value

pub const MAX_10_EXP: i32 = 38i32

Maximum possible bf16 power of 10 exponent

pub const MAX_EXP: i32 = 128i32

Maximum possible bf16 power of 2 exponent

pub const MIN: bf16 = _

Smallest finite bf16 value

pub const MIN_10_EXP: i32 = -37i32

Minimum possible normal bf16 power of 10 exponent

pub const MIN_EXP: i32 = -125i32

One greater than the minimum possible normal bf16 power of 2 exponent

pub const MIN_POSITIVE: bf16 = _

Smallest positive normal bf16 value

pub const NAN: bf16 = _

bf16 Not a Number (NaN)

pub const NEG_INFINITY: bf16 = _

bf16 negative infinity (-∞).

pub const RADIX: u32 = 2u32

The radix or base of the internal representation of bf16

pub const MIN_POSITIVE_SUBNORMAL: bf16 = _

Minimum positive subnormal bf16 value

pub const MAX_SUBNORMAL: bf16 = _

Maximum subnormal bf16 value

pub const ONE: bf16 = _

bf16 1

pub const ZERO: bf16 = _

bf16 0

pub const NEG_ZERO: bf16 = _

bf16 -0

pub const NEG_ONE: bf16 = _

bf16 -1

pub const E: bf16 = _

bf16 Euler’s number (ℯ)

pub const PI: bf16 = _

bf16 Archimedes’ constant (π)

pub const FRAC_1_PI: bf16 = _

bf16 1/π

pub const FRAC_1_SQRT_2: bf16 = _

bf16 1/√2

pub const FRAC_2_PI: bf16 = _

bf16 2/π

pub const FRAC_2_SQRT_PI: bf16 = _

bf16 2/√π

pub const FRAC_PI_2: bf16 = _

bf16 π/2

pub const FRAC_PI_3: bf16 = _

bf16 π/3

pub const FRAC_PI_4: bf16 = _

bf16 π/4

pub const FRAC_PI_6: bf16 = _

bf16 π/6

pub const FRAC_PI_8: bf16 = _

bf16 π/8

pub const LN_10: bf16 = _

bf16 𝗅𝗇 10

pub const LN_2: bf16 = _

bf16 𝗅𝗇 2

pub const LOG10_E: bf16 = _

bf16 𝗅𝗈𝗀₁₀ℯ

pub const LOG10_2: bf16 = _

bf16 𝗅𝗈𝗀₁₀2

pub const LOG2_E: bf16 = _

bf16 𝗅𝗈𝗀₂ℯ

pub const LOG2_10: bf16 = _

bf16 𝗅𝗈𝗀₂10

pub const SQRT_2: bf16 = _

bf16 √2

Trait Implementations

impl Add<&bf16> for &bf16

type Output = <bf16 as Add<bf16>>::Output

The resulting type after applying the + operator.

fn add(self, rhs: &bf16) -> Self::Output

Performs the + operation.

impl Add<&bf16> for bf16

type Output = <bf16 as Add<bf16>>::Output

The resulting type after applying the + operator.

fn add(self, rhs: &bf16) -> Self::Output

Performs the + operation.

impl Add<bf16> for &bf16

type Output = <bf16 as Add<bf16>>::Output

The resulting type after applying the + operator.

fn add(self, rhs: bf16) -> Self::Output

Performs the + operation.

impl Add<bf16> for bf16

type Output = bf16

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl AddAssign<&bf16> for bf16

fn add_assign(&mut self, rhs: &bf16)

Performs the += operation.

impl AddAssign<bf16> for bf16

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Binary for bf16

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

Formats the value using the given formatter.

impl Clone for bf16

fn clone(&self) -> bf16

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for bf16

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

Formats the value using the given formatter.

impl Default for bf16

fn default() -> bf16

Returns the “default value” for a type.

impl Display for bf16

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

Formats the value using the given formatter.

impl Div<&bf16> for &bf16

type Output = <bf16 as Div<bf16>>::Output

The resulting type after applying the / operator.

fn div(self, rhs: &bf16) -> Self::Output

Performs the / operation.

impl Div<&bf16> for bf16

type Output = <bf16 as Div<bf16>>::Output

The resulting type after applying the / operator.

fn div(self, rhs: &bf16) -> Self::Output

Performs the / operation.

impl Div<bf16> for &bf16

type Output = <bf16 as Div<bf16>>::Output

The resulting type after applying the / operator.

fn div(self, rhs: bf16) -> Self::Output

Performs the / operation.

impl Div<bf16> for bf16

type Output = bf16

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self::Output

Performs the / operation.

impl DivAssign<&bf16> for bf16

fn div_assign(&mut self, rhs: &bf16)

Performs the /= operation.

impl DivAssign<bf16> for bf16

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl From<bf16> for f32

fn from(x: bf16) -> f32

Converts to this type from the input type.

impl From<bf16> for f64

fn from(x: bf16) -> f64

Converts to this type from the input type.

impl From<i8> for bf16

fn from(x: i8) -> bf16

Converts to this type from the input type.

impl From<u8> for bf16

fn from(x: u8) -> bf16

Converts to this type from the input type.

impl FromStr for bf16

type Err = ParseFloatError

The associated error which can be returned from parsing.

fn from_str(src: &str) -> Result<bf16, ParseFloatError>

Parses a string s to return a value of this type.

impl LowerExp for bf16

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

Formats the value using the given formatter.

impl LowerHex for bf16

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

Formats the value using the given formatter.

impl Mul<&bf16> for &bf16

type Output = <bf16 as Mul<bf16>>::Output

The resulting type after applying the * operator.

fn mul(self, rhs: &bf16) -> Self::Output

Performs the * operation.

impl Mul<&bf16> for bf16

type Output = <bf16 as Mul<bf16>>::Output

The resulting type after applying the * operator.

fn mul(self, rhs: &bf16) -> Self::Output

Performs the * operation.

impl Mul<bf16> for &bf16

type Output = <bf16 as Mul<bf16>>::Output

The resulting type after applying the * operator.

fn mul(self, rhs: bf16) -> Self::Output

Performs the * operation.

impl Mul<bf16> for bf16

type Output = bf16

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl MulAssign<&bf16> for bf16

fn mul_assign(&mut self, rhs: &bf16)

Performs the *= operation.

impl MulAssign<bf16> for bf16

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Neg for &bf16

type Output = <bf16 as Neg>::Output

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Neg for bf16

type Output = bf16

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Octal for bf16

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

Formats the value using the given formatter.

impl PartialEq<bf16> for bf16

fn eq(&self, other: &bf16) -> bool

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

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

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

impl PartialOrd<bf16> for bf16

fn partial_cmp(&self, other: &bf16) -> Option<Ordering>

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

fn lt(&self, other: &bf16) -> bool

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

fn le(&self, other: &bf16) -> bool

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

fn gt(&self, other: &bf16) -> bool

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

fn ge(&self, other: &bf16) -> bool

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

impl<'a> Product<&'a bf16> for bf16

fn product<I: Iterator<Item = &'a bf16>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl Product<bf16> for bf16

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

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl Rem<&bf16> for &bf16

type Output = <bf16 as Rem<bf16>>::Output

The resulting type after applying the % operator.

fn rem(self, rhs: &bf16) -> Self::Output

Performs the % operation.

impl Rem<&bf16> for bf16

type Output = <bf16 as Rem<bf16>>::Output

The resulting type after applying the % operator.

fn rem(self, rhs: &bf16) -> Self::Output

Performs the % operation.

impl Rem<bf16> for &bf16

type Output = <bf16 as Rem<bf16>>::Output

The resulting type after applying the % operator.

fn rem(self, rhs: bf16) -> Self::Output

Performs the % operation.

impl Rem<bf16> for bf16

type Output = bf16

The resulting type after applying the % operator.

fn rem(self, rhs: Self) -> Self::Output

Performs the % operation.

impl RemAssign<&bf16> for bf16

fn rem_assign(&mut self, rhs: &bf16)

Performs the %= operation.

impl RemAssign<bf16> for bf16

fn rem_assign(&mut self, rhs: Self)

Performs the %= operation.

impl Sub<&bf16> for &bf16

type Output = <bf16 as Sub<bf16>>::Output

The resulting type after applying the - operator.

fn sub(self, rhs: &bf16) -> Self::Output

Performs the - operation.

impl Sub<&bf16> for bf16

type Output = <bf16 as Sub<bf16>>::Output

The resulting type after applying the - operator.

fn sub(self, rhs: &bf16) -> Self::Output

Performs the - operation.

impl Sub<bf16> for &bf16

type Output = <bf16 as Sub<bf16>>::Output

The resulting type after applying the - operator.

fn sub(self, rhs: bf16) -> Self::Output

Performs the - operation.

impl Sub<bf16> for bf16

type Output = bf16

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl SubAssign<&bf16> for bf16

fn sub_assign(&mut self, rhs: &bf16)

Performs the -= operation.

impl SubAssign<bf16> for bf16

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'a> Sum<&'a bf16> for bf16

fn sum<I: Iterator<Item = &'a bf16>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl Sum<bf16> for bf16

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

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl UpperExp for bf16

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

Formats the value using the given formatter.

impl UpperHex for bf16

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

Formats the value using the given formatter.

impl Copy for bf16