Struct half::bf16

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pub struct bf16(/* private fields */);
Expand description

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.

Implementations§

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impl bf16

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

Constructs a bf16 value from the raw bits.

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pub fn from_f32(value: f32) -> bf16

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

This operation is lossy. 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.

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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.

This operation is lossy. 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.

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pub fn from_f64(value: f64) -> bf16

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

This operation is lossy. 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.

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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.

This operation is lossy. 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.

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pub const fn to_bits(self) -> u16

Converts a bf16 into the underlying bit representation.

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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]);
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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]);
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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]
});
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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));
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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));
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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));
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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.

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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.

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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.

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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.

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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());
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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());
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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());
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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());
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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);
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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());
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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());
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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());
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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());
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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);
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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);
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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());
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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()));
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pub const DIGITS: u32 = 2u32

Approximate number of bf16 significant digits in base 10

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pub const EPSILON: bf16 = _

bf16 machine epsilon value

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

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pub const INFINITY: bf16 = _

bf16 positive Infinity (+∞)

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pub const MANTISSA_DIGITS: u32 = 8u32

Number of bf16 significant digits in base 2

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pub const MAX: bf16 = _

Largest finite bf16 value

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pub const MAX_10_EXP: i32 = 38i32

Maximum possible bf16 power of 10 exponent

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pub const MAX_EXP: i32 = 128i32

Maximum possible bf16 power of 2 exponent

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pub const MIN: bf16 = _

Smallest finite bf16 value

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pub const MIN_10_EXP: i32 = -37i32

Minimum possible normal bf16 power of 10 exponent

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pub const MIN_EXP: i32 = -125i32

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

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pub const MIN_POSITIVE: bf16 = _

Smallest positive normal bf16 value

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pub const NAN: bf16 = _

bf16 Not a Number (NaN)

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pub const NEG_INFINITY: bf16 = _

bf16 negative infinity (-∞).

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pub const RADIX: u32 = 2u32

The radix or base of the internal representation of bf16

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pub const MIN_POSITIVE_SUBNORMAL: bf16 = _

Minimum positive subnormal bf16 value

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pub const MAX_SUBNORMAL: bf16 = _

Maximum subnormal bf16 value

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pub const ONE: bf16 = _

bf16 1

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pub const ZERO: bf16 = _

bf16 0

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pub const NEG_ZERO: bf16 = _

bf16 -0

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pub const NEG_ONE: bf16 = _

bf16 -1

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pub const E: bf16 = _

bf16 Euler’s number (ℯ)

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pub const PI: bf16 = _

bf16 Archimedes’ constant (π)

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pub const FRAC_1_PI: bf16 = _

bf16 1/π

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pub const FRAC_1_SQRT_2: bf16 = _

bf16 1/√2

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pub const FRAC_2_PI: bf16 = _

bf16 2/π

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pub const FRAC_2_SQRT_PI: bf16 = _

bf16 2/√π

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pub const FRAC_PI_2: bf16 = _

bf16 π/2

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pub const FRAC_PI_3: bf16 = _

bf16 π/3

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pub const FRAC_PI_4: bf16 = _

bf16 π/4

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pub const FRAC_PI_6: bf16 = _

bf16 π/6

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pub const FRAC_PI_8: bf16 = _

bf16 π/8

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pub const LN_10: bf16 = _

bf16 𝗅𝗇 10

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pub const LN_2: bf16 = _

bf16 𝗅𝗇 2

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pub const LOG10_E: bf16 = _

bf16 𝗅𝗈𝗀₁₀ℯ

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pub const LOG10_2: bf16 = _

bf16 𝗅𝗈𝗀₁₀2

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pub const LOG2_E: bf16 = _

bf16 𝗅𝗈𝗀₂ℯ

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pub const LOG2_10: bf16 = _

bf16 𝗅𝗈𝗀₂10

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pub const SQRT_2: bf16 = _

bf16 √2

Trait Implementations§

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impl Add<&bf16> for &bf16

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type Output = <bf16 as Add>::Output

The resulting type after applying the + operator.
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fn add(self, rhs: &bf16) -> Self::Output

Performs the + operation. Read more
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impl Add<&bf16> for bf16

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type Output = <bf16 as Add>::Output

The resulting type after applying the + operator.
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fn add(self, rhs: &bf16) -> Self::Output

Performs the + operation. Read more
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impl Add<bf16> for &bf16

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type Output = <bf16 as Add>::Output

The resulting type after applying the + operator.
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fn add(self, rhs: bf16) -> Self::Output

Performs the + operation. Read more
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impl Add for bf16

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type Output = bf16

The resulting type after applying the + operator.
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fn add(self, rhs: Self) -> Self::Output

Performs the + operation. Read more
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impl AddAssign<&bf16> for bf16

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

Performs the += operation. Read more
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impl AddAssign for bf16

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fn add_assign(&mut self, rhs: Self)

Performs the += operation. Read more
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impl AsPrimitive<bf16> for bf16

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for f16

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for f32

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for f64

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for i16

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for i32

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for i64

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for i8

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for isize

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for u16

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for u32

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for u64

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for u8

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<bf16> for usize

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fn as_(self) -> bf16

Convert a value to another, using the as operator.
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impl AsPrimitive<f16> for bf16

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fn as_(self) -> f16

Convert a value to another, using the as operator.
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impl AsPrimitive<f32> for bf16

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fn as_(self) -> f32

Convert a value to another, using the as operator.
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impl AsPrimitive<f64> for bf16

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fn as_(self) -> f64

Convert a value to another, using the as operator.
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impl AsPrimitive<i16> for bf16

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fn as_(self) -> i16

Convert a value to another, using the as operator.
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impl AsPrimitive<i32> for bf16

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fn as_(self) -> i32

Convert a value to another, using the as operator.
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impl AsPrimitive<i64> for bf16

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fn as_(self) -> i64

Convert a value to another, using the as operator.
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impl AsPrimitive<i8> for bf16

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fn as_(self) -> i8

Convert a value to another, using the as operator.
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impl AsPrimitive<isize> for bf16

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fn as_(self) -> isize

Convert a value to another, using the as operator.
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impl AsPrimitive<u16> for bf16

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fn as_(self) -> u16

Convert a value to another, using the as operator.
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impl AsPrimitive<u32> for bf16

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fn as_(self) -> u32

Convert a value to another, using the as operator.
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impl AsPrimitive<u64> for bf16

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fn as_(self) -> u64

Convert a value to another, using the as operator.
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impl AsPrimitive<u8> for bf16

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fn as_(self) -> u8

Convert a value to another, using the as operator.
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impl AsPrimitive<usize> for bf16

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fn as_(self) -> usize

Convert a value to another, using the as operator.
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impl Binary for bf16

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

Formats the value using the given formatter. Read more
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impl Bounded for bf16

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fn min_value() -> Self

Returns the smallest finite number this type can represent
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fn max_value() -> Self

Returns the largest finite number this type can represent
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impl Clone for bf16

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fn clone(&self) -> bf16

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl Debug for bf16

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

Formats the value using the given formatter. Read more
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impl Default for bf16

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fn default() -> bf16

Returns the “default value” for a type. Read more
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impl Display for bf16

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

Formats the value using the given formatter. Read more
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impl Div<&bf16> for &bf16

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type Output = <bf16 as Div>::Output

The resulting type after applying the / operator.
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fn div(self, rhs: &bf16) -> Self::Output

Performs the / operation. Read more
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impl Div<&bf16> for bf16

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type Output = <bf16 as Div>::Output

The resulting type after applying the / operator.
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fn div(self, rhs: &bf16) -> Self::Output

Performs the / operation. Read more
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impl Div<bf16> for &bf16

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type Output = <bf16 as Div>::Output

The resulting type after applying the / operator.
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fn div(self, rhs: bf16) -> Self::Output

Performs the / operation. Read more
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impl Div for bf16

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type Output = bf16

The resulting type after applying the / operator.
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fn div(self, rhs: Self) -> Self::Output

Performs the / operation. Read more
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impl DivAssign<&bf16> for bf16

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

Performs the /= operation. Read more
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impl DivAssign for bf16

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fn div_assign(&mut self, rhs: Self)

Performs the /= operation. Read more
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impl Float for bf16

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fn nan() -> Self

Returns the NaN value. Read more
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fn infinity() -> Self

Returns the infinite value. Read more
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fn neg_infinity() -> Self

Returns the negative infinite value. Read more
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fn neg_zero() -> Self

Returns -0.0. Read more
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fn min_value() -> Self

Returns the smallest finite value that this type can represent. Read more
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fn min_positive_value() -> Self

Returns the smallest positive, normalized value that this type can represent. Read more
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fn epsilon() -> Self

Returns epsilon, a small positive value. Read more
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fn max_value() -> Self

Returns the largest finite value that this type can represent. Read more
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fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise. Read more
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fn is_infinite(self) -> bool

Returns true if this value is positive infinity or negative infinity and false otherwise. Read more
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fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN. Read more
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fn is_normal(self) -> bool

Returns true if the number is neither zero, infinite, subnormal, or NaN. Read more
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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. Read more
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fn floor(self) -> Self

Returns the largest integer less than or equal to a number. Read more
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fn ceil(self) -> Self

Returns the smallest integer greater than or equal to a number. Read more
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fn round(self) -> Self

Returns the nearest integer to a number. Round half-way cases away from 0.0. Read more
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fn trunc(self) -> Self

Return the integer part of a number. Read more
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fn fract(self) -> Self

Returns the fractional part of a number. Read more
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fn abs(self) -> Self

Computes the absolute value of self. Returns Float::nan() if the number is Float::nan(). Read more
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fn signum(self) -> Self

Returns a number that represents the sign of self. Read more
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fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0, Float::infinity(), and since Rust 1.20 also Float::nan(). Read more
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fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0, Float::neg_infinity(), and since Rust 1.20 also -Float::nan(). Read more
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fn mul_add(self, a: Self, b: Self) -> Self

Fused multiply-add. Computes (self * a) + b with only one rounding error, yielding a more accurate result than an unfused multiply-add. Read more
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fn recip(self) -> Self

Take the reciprocal (inverse) of a number, 1/x. Read more
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fn powi(self, n: i32) -> Self

Raise a number to an integer power. Read more
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fn powf(self, n: Self) -> Self

Raise a number to a floating point power. Read more
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fn sqrt(self) -> Self

Take the square root of a number. Read more
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fn exp(self) -> Self

Returns e^(self), (the exponential function). Read more
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fn exp2(self) -> Self

Returns 2^(self). Read more
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fn ln(self) -> Self

Returns the natural logarithm of the number. Read more
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fn log(self, base: Self) -> Self

Returns the logarithm of the number with respect to an arbitrary base. Read more
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fn log2(self) -> Self

Returns the base 2 logarithm of the number. Read more
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fn log10(self) -> Self

Returns the base 10 logarithm of the number. Read more
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fn to_degrees(self) -> Self

Converts radians to degrees. Read more
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fn to_radians(self) -> Self

Converts degrees to radians. Read more
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fn max(self, other: Self) -> Self

Returns the maximum of the two numbers. Read more
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fn min(self, other: Self) -> Self

Returns the minimum of the two numbers. Read more
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fn abs_sub(self, other: Self) -> Self

The positive difference of two numbers. Read more
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fn cbrt(self) -> Self

Take the cubic root of a number. Read more
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fn hypot(self, other: Self) -> Self

Calculate the length of the hypotenuse of a right-angle triangle given legs of length x and y. Read more
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fn sin(self) -> Self

Computes the sine of a number (in radians). Read more
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fn cos(self) -> Self

Computes the cosine of a number (in radians). Read more
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fn tan(self) -> Self

Computes the tangent of a number (in radians). Read more
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fn asin(self) -> Self

Computes the arcsine of a number. Return value is in radians in the range [-pi/2, pi/2] or NaN if the number is outside the range [-1, 1]. Read more
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fn acos(self) -> Self

Computes the arccosine of a number. Return value is in radians in the range [0, pi] or NaN if the number is outside the range [-1, 1]. Read more
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fn atan(self) -> Self

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2]; Read more
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fn atan2(self, other: Self) -> Self

Computes the four quadrant arctangent of self (y) and other (x). Read more
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fn sin_cos(self) -> (Self, Self)

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)). Read more
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fn exp_m1(self) -> Self

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero. Read more
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fn ln_1p(self) -> Self

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately. Read more
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fn sinh(self) -> Self

Hyperbolic sine function. Read more
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fn cosh(self) -> Self

Hyperbolic cosine function. Read more
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fn tanh(self) -> Self

Hyperbolic tangent function. Read more
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fn asinh(self) -> Self

Inverse hyperbolic sine function. Read more
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fn acosh(self) -> Self

Inverse hyperbolic cosine function. Read more
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fn atanh(self) -> Self

Inverse hyperbolic tangent function. Read more
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fn integer_decode(self) -> (u64, i16, i8)

Returns the mantissa, base 2 exponent, and sign as integers, respectively. The original number can be recovered by sign * mantissa * 2 ^ exponent. Read more
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fn copysign(self, sign: Self) -> Self

Returns a number composed of the magnitude of self and the sign of sign. Read more
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impl FloatConst for bf16

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fn E() -> Self

Return Euler’s number.
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fn FRAC_1_PI() -> Self

Return 1.0 / π.
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fn FRAC_1_SQRT_2() -> Self

Return 1.0 / sqrt(2.0).
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fn FRAC_2_PI() -> Self

Return 2.0 / π.
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fn FRAC_2_SQRT_PI() -> Self

Return 2.0 / sqrt(π).
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fn FRAC_PI_2() -> Self

Return π / 2.0.
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fn FRAC_PI_3() -> Self

Return π / 3.0.
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fn FRAC_PI_4() -> Self

Return π / 4.0.
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fn FRAC_PI_6() -> Self

Return π / 6.0.
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fn FRAC_PI_8() -> Self

Return π / 8.0.
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fn LN_10() -> Self

Return ln(10.0).
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fn LN_2() -> Self

Return ln(2.0).
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fn LOG10_E() -> Self

Return log10(e).
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fn LOG2_E() -> Self

Return log2(e).
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fn PI() -> Self

Return Archimedes’ constant π.
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fn SQRT_2() -> Self

Return sqrt(2.0).
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fn LOG10_2() -> Self
where Self: Sized + Div<Self, Output = Self>,

Return log10(2.0).
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fn LOG2_10() -> Self
where Self: Sized + Div<Self, Output = Self>,

Return log2(10.0).
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fn TAU() -> Self
where Self: Sized + Add<Output = Self>,

Return the full circle constant τ.
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impl FloatCore for bf16

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fn infinity() -> Self

Returns positive infinity. Read more
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fn neg_infinity() -> Self

Returns negative infinity. Read more
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fn nan() -> Self

Returns NaN. Read more
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fn neg_zero() -> Self

Returns -0.0. Read more
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fn min_value() -> Self

Returns the smallest finite value that this type can represent. Read more
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fn min_positive_value() -> Self

Returns the smallest positive, normalized value that this type can represent. Read more
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fn epsilon() -> Self

Returns epsilon, a small positive value. Read more
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fn max_value() -> Self

Returns the largest finite value that this type can represent. Read more
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fn is_nan(self) -> bool

Returns true if the number is NaN. Read more
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fn is_infinite(self) -> bool

Returns true if the number is infinite. Read more
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fn is_finite(self) -> bool

Returns true if the number is neither infinite or NaN. Read more
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fn is_normal(self) -> bool

Returns true if the number is neither zero, infinite, subnormal or NaN. Read more
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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. Read more
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fn floor(self) -> Self

Returns the largest integer less than or equal to a number. Read more
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fn ceil(self) -> Self

Returns the smallest integer greater than or equal to a number. Read more
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fn round(self) -> Self

Returns the nearest integer to a number. Round half-way cases away from 0.0. Read more
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fn trunc(self) -> Self

Return the integer part of a number. Read more
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fn fract(self) -> Self

Returns the fractional part of a number. Read more
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fn abs(self) -> Self

Computes the absolute value of self. Returns FloatCore::nan() if the number is FloatCore::nan(). Read more
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fn signum(self) -> Self

Returns a number that represents the sign of self. Read more
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fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0 and FloatCore::infinity(), and since Rust 1.20 also FloatCore::nan(). Read more
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fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0 and FloatCore::neg_infinity(), and since Rust 1.20 also -FloatCore::nan(). Read more
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fn min(self, other: Self) -> Self

Returns the minimum of the two numbers. Read more
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fn max(self, other: Self) -> Self

Returns the maximum of the two numbers. Read more
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fn recip(self) -> Self

Returns the reciprocal (multiplicative inverse) of the number. Read more
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fn powi(self, exp: i32) -> Self

Raise a number to an integer power. Read more
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fn to_degrees(self) -> Self

Converts to degrees, assuming the number is in radians. Read more
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fn to_radians(self) -> Self

Converts to radians, assuming the number is in degrees. Read more
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fn integer_decode(self) -> (u64, i16, i8)

Returns the mantissa, base 2 exponent, and sign as integers, respectively. The original number can be recovered by sign * mantissa * 2 ^ exponent. Read more
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impl From<bf16> for f32

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fn from(x: bf16) -> f32

Converts to this type from the input type.
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impl From<bf16> for f64

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fn from(x: bf16) -> f64

Converts to this type from the input type.
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impl From<i8> for bf16

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fn from(x: i8) -> bf16

Converts to this type from the input type.
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impl From<u8> for bf16

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fn from(x: u8) -> bf16

Converts to this type from the input type.
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impl FromPrimitive for bf16

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fn from_i64(n: i64) -> Option<Self>

Converts an i64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_u64(n: u64) -> Option<Self>

Converts an u64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_i8(n: i8) -> Option<Self>

Converts an i8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_u8(n: u8) -> Option<Self>

Converts an u8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_i16(n: i16) -> Option<Self>

Converts an i16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_u16(n: u16) -> Option<Self>

Converts an u16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_i32(n: i32) -> Option<Self>

Converts an i32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_u32(n: u32) -> Option<Self>

Converts an u32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_f32(n: f32) -> Option<Self>

Converts a f32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_f64(n: f64) -> Option<Self>

Converts a f64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more
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fn from_isize(n: isize) -> Option<Self>

Converts an isize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_i128(n: i128) -> Option<Self>

Converts an i128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more
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fn from_usize(n: usize) -> Option<Self>

Converts a usize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_u128(n: u128) -> Option<Self>

Converts an u128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more
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impl FromStr for bf16

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type Err = ParseFloatError

The associated error which can be returned from parsing.
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fn from_str(src: &str) -> Result<bf16, ParseFloatError>

Parses a string s to return a value of this type. Read more
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impl LowerExp for bf16

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

Formats the value using the given formatter. Read more
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impl LowerHex for bf16

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

Formats the value using the given formatter. Read more
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impl Mul<&bf16> for &bf16

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type Output = <bf16 as Mul>::Output

The resulting type after applying the * operator.
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fn mul(self, rhs: &bf16) -> Self::Output

Performs the * operation. Read more
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impl Mul<&bf16> for bf16

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type Output = <bf16 as Mul>::Output

The resulting type after applying the * operator.
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fn mul(self, rhs: &bf16) -> Self::Output

Performs the * operation. Read more
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impl Mul<bf16> for &bf16

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type Output = <bf16 as Mul>::Output

The resulting type after applying the * operator.
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fn mul(self, rhs: bf16) -> Self::Output

Performs the * operation. Read more
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impl Mul for bf16

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type Output = bf16

The resulting type after applying the * operator.
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fn mul(self, rhs: Self) -> Self::Output

Performs the * operation. Read more
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impl MulAssign<&bf16> for bf16

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

Performs the *= operation. Read more
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impl MulAssign for bf16

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fn mul_assign(&mut self, rhs: Self)

Performs the *= operation. Read more
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impl Neg for &bf16

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type Output = <bf16 as Neg>::Output

The resulting type after applying the - operator.
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fn neg(self) -> Self::Output

Performs the unary - operation. Read more
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impl Neg for bf16

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type Output = bf16

The resulting type after applying the - operator.
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fn neg(self) -> Self::Output

Performs the unary - operation. Read more
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impl Num for bf16

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type FromStrRadixErr = <f32 as Num>::FromStrRadixErr

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fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>

Convert from a string and radix (typically 2..=36). Read more
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impl NumCast for bf16

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fn from<T: ToPrimitive>(n: T) -> Option<Self>

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait. If the source value cannot be represented by the target type, then None is returned. Read more
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impl Octal for bf16

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

Formats the value using the given formatter. Read more
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impl One for bf16

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fn one() -> Self

Returns the multiplicative identity element of Self, 1. Read more
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fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.
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fn is_one(&self) -> bool
where Self: PartialEq,

Returns true if self is equal to the multiplicative identity. Read more
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impl PartialEq for bf16

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

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl PartialOrd for bf16

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

Tests less than (for self and other) and is used by the < operator. Read more
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fn le(&self, other: &bf16) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator. Read more
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fn gt(&self, other: &bf16) -> bool

Tests greater than (for self and other) and is used by the > operator. Read more
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fn ge(&self, other: &bf16) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator. Read more
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impl<'a> Product<&'a bf16> for bf16

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

Takes an iterator and generates Self from the elements by multiplying the items.
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impl Product for bf16

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

Takes an iterator and generates Self from the elements by multiplying the items.
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impl Rem<&bf16> for &bf16

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type Output = <bf16 as Rem>::Output

The resulting type after applying the % operator.
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fn rem(self, rhs: &bf16) -> Self::Output

Performs the % operation. Read more
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impl Rem<&bf16> for bf16

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type Output = <bf16 as Rem>::Output

The resulting type after applying the % operator.
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fn rem(self, rhs: &bf16) -> Self::Output

Performs the % operation. Read more
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impl Rem<bf16> for &bf16

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type Output = <bf16 as Rem>::Output

The resulting type after applying the % operator.
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fn rem(self, rhs: bf16) -> Self::Output

Performs the % operation. Read more
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impl Rem for bf16

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type Output = bf16

The resulting type after applying the % operator.
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fn rem(self, rhs: Self) -> Self::Output

Performs the % operation. Read more
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impl RemAssign<&bf16> for bf16

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

Performs the %= operation. Read more
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impl RemAssign for bf16

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fn rem_assign(&mut self, rhs: Self)

Performs the %= operation. Read more
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impl Sub<&bf16> for &bf16

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type Output = <bf16 as Sub>::Output

The resulting type after applying the - operator.
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fn sub(self, rhs: &bf16) -> Self::Output

Performs the - operation. Read more
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impl Sub<&bf16> for bf16

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type Output = <bf16 as Sub>::Output

The resulting type after applying the - operator.
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fn sub(self, rhs: &bf16) -> Self::Output

Performs the - operation. Read more
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impl Sub<bf16> for &bf16

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type Output = <bf16 as Sub>::Output

The resulting type after applying the - operator.
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fn sub(self, rhs: bf16) -> Self::Output

Performs the - operation. Read more
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impl Sub for bf16

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type Output = bf16

The resulting type after applying the - operator.
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fn sub(self, rhs: Self) -> Self::Output

Performs the - operation. Read more
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impl SubAssign<&bf16> for bf16

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

Performs the -= operation. Read more
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impl SubAssign for bf16

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fn sub_assign(&mut self, rhs: Self)

Performs the -= operation. Read more
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impl<'a> Sum<&'a bf16> for bf16

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

Takes an iterator and generates Self from the elements by “summing up” the items.
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impl Sum for bf16

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

Takes an iterator and generates Self from the elements by “summing up” the items.
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impl ToPrimitive for bf16

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fn to_i64(&self) -> Option<i64>

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned.
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fn to_u64(&self) -> Option<u64>

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned.
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fn to_i8(&self) -> Option<i8>

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned.
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fn to_u8(&self) -> Option<u8>

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned.
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fn to_i16(&self) -> Option<i16>

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned.
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fn to_u16(&self) -> Option<u16>

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned.
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fn to_i32(&self) -> Option<i32>

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned.
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fn to_u32(&self) -> Option<u32>

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned.
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fn to_f32(&self) -> Option<f32>

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32.
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fn to_f64(&self) -> Option<f64>

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64. Read more
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fn to_isize(&self) -> Option<isize>

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned.
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fn to_i128(&self) -> Option<i128>

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned. Read more
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fn to_usize(&self) -> Option<usize>

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned.
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fn to_u128(&self) -> Option<u128>

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned. Read more
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impl UpperExp for bf16

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

Formats the value using the given formatter. Read more
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impl UpperHex for bf16

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

Formats the value using the given formatter. Read more
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impl Zero for bf16

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fn zero() -> Self

Returns the additive identity element of Self, 0. Read more
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fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.
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fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.
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impl Copy for bf16

Auto Trait Implementations§

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impl Freeze for bf16

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impl RefUnwindSafe for bf16

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impl Send for bf16

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impl Sync for bf16

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impl Unpin for bf16

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impl UnwindSafe for bf16

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> CloneToUninit for T
where T: Clone,

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default unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. Read more
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impl<T> CloneToUninit for T
where T: Copy,

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unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. 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> LowerBounded for T
where T: Bounded,

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fn min_value() -> T

Returns the smallest finite number this type can represent
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impl<T> Real for T
where T: Float,

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fn min_value() -> T

Returns the smallest finite value that this type can represent. Read more
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fn min_positive_value() -> T

Returns the smallest positive, normalized value that this type can represent. Read more
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fn epsilon() -> T

Returns epsilon, a small positive value. Read more
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fn max_value() -> T

Returns the largest finite value that this type can represent. Read more
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fn floor(self) -> T

Returns the largest integer less than or equal to a number. Read more
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fn ceil(self) -> T

Returns the smallest integer greater than or equal to a number. Read more
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fn round(self) -> T

Returns the nearest integer to a number. Round half-way cases away from 0.0. Read more
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fn trunc(self) -> T

Return the integer part of a number. Read more
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fn fract(self) -> T

Returns the fractional part of a number. Read more
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fn abs(self) -> T

Computes the absolute value of self. Returns Float::nan() if the number is Float::nan(). Read more
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fn signum(self) -> T

Returns a number that represents the sign of self. Read more
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fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0, Float::infinity(), and with newer versions of Rust f64::NAN. Read more
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fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0, Float::neg_infinity(), and with newer versions of Rust -f64::NAN. Read more
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fn mul_add(self, a: T, b: T) -> T

Fused multiply-add. Computes (self * a) + b with only one rounding error, yielding a more accurate result than an unfused multiply-add. Read more
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fn recip(self) -> T

Take the reciprocal (inverse) of a number, 1/x. Read more
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fn powi(self, n: i32) -> T

Raise a number to an integer power. Read more
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fn powf(self, n: T) -> T

Raise a number to a real number power. Read more
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fn sqrt(self) -> T

Take the square root of a number. Read more
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fn exp(self) -> T

Returns e^(self), (the exponential function). Read more
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fn exp2(self) -> T

Returns 2^(self). Read more
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fn ln(self) -> T

Returns the natural logarithm of the number. Read more
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fn log(self, base: T) -> T

Returns the logarithm of the number with respect to an arbitrary base. Read more
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fn log2(self) -> T

Returns the base 2 logarithm of the number. Read more
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fn log10(self) -> T

Returns the base 10 logarithm of the number. Read more
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fn to_degrees(self) -> T

Converts radians to degrees. Read more
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fn to_radians(self) -> T

Converts degrees to radians. Read more
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fn max(self, other: T) -> T

Returns the maximum of the two numbers. Read more
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fn min(self, other: T) -> T

Returns the minimum of the two numbers. Read more
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fn abs_sub(self, other: T) -> T

The positive difference of two numbers. Read more
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fn cbrt(self) -> T

Take the cubic root of a number. Read more
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fn hypot(self, other: T) -> T

Calculate the length of the hypotenuse of a right-angle triangle given legs of length x and y. Read more
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fn sin(self) -> T

Computes the sine of a number (in radians). Read more
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fn cos(self) -> T

Computes the cosine of a number (in radians). Read more
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fn tan(self) -> T

Computes the tangent of a number (in radians). Read more
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fn asin(self) -> T

Computes the arcsine of a number. Return value is in radians in the range [-pi/2, pi/2] or NaN if the number is outside the range [-1, 1]. Read more
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fn acos(self) -> T

Computes the arccosine of a number. Return value is in radians in the range [0, pi] or NaN if the number is outside the range [-1, 1]. Read more
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fn atan(self) -> T

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2]; Read more
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fn atan2(self, other: T) -> T

Computes the four quadrant arctangent of self (y) and other (x). Read more
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fn sin_cos(self) -> (T, T)

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)). Read more
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fn exp_m1(self) -> T

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero. Read more
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fn ln_1p(self) -> T

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately. Read more
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fn sinh(self) -> T

Hyperbolic sine function. Read more
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fn cosh(self) -> T

Hyperbolic cosine function. Read more
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fn tanh(self) -> T

Hyperbolic tangent function. Read more
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fn asinh(self) -> T

Inverse hyperbolic sine function. Read more
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fn acosh(self) -> T

Inverse hyperbolic cosine function. Read more
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fn atanh(self) -> T

Inverse hyperbolic tangent function. Read more
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> ToString for T
where T: Display + ?Sized,

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default fn to_string(&self) -> String

Converts the given value to a String. Read more
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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.
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impl<T> UpperBounded for T
where T: Bounded,

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fn max_value() -> T

Returns the largest finite number this type can represent
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impl<T> NumAssign for T
where T: Num + NumAssignOps,

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impl<T, Rhs> NumAssignOps<Rhs> for T
where T: AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>,

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impl<T> NumAssignRef for T
where T: NumAssign + for<'r> NumAssignOps<&'r T>,

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impl<T, Rhs, Output> NumOps<Rhs, Output> for T
where T: Sub<Rhs, Output = Output> + Mul<Rhs, Output = Output> + Div<Rhs, Output = Output> + Add<Rhs, Output = Output> + Rem<Rhs, Output = Output>,

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impl<T> NumRef for T
where T: Num + for<'r> NumOps<&'r T>,

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impl<T, Base> RefNum<Base> for T
where T: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base>,