impl bf16

const fn from_bits(bits: u16) -> bf16

Constructs a [struct@bf16] value from the raw bits.

fn from_f32(value: f32) -> bf16

Constructs a [struct@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.

const fn from_f32_const(value: f32) -> bf16

Constructs a [struct@bf16] value from a 32-bit floating point value.

This function is identical to [from_f32][Self::from_f32] except it never uses hardware intrinsics, which allows it to be const. [from_f32][Self::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.

fn from_f64(value: f64) -> bf16

Constructs a [struct@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.

const fn from_f64_const(value: f64) -> bf16

Constructs a [struct@bf16] value from a 64-bit floating point value.

This function is identical to [from_f64][Self::from_f64] except it never uses hardware intrinsics, which allows it to be const. [from_f64][Self::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.

const fn to_bits(self) -> u16

Converts a [struct@bf16] into the underlying bit representation.

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

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

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

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

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][bf16::to_be_bytes] or [to_le_bytes][bf16::to_le_bytes], as appropriate, instead.

Examples

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

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

# use half::prelude::*;
let value = bf16::from_le_bytes([0x48, 0x41]);
assert_eq!(value, bf16::from_f32(12.5));

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

# use half::prelude::*;
let value = bf16::from_be_bytes([0x41, 0x48]);
assert_eq!(value, bf16::from_f32(12.5));

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][bf16::from_be_bytes] or [from_le_bytes][bf16::from_le_bytes], as appropriate instead.

Examples

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

fn to_f32(self) -> f32

Converts a [struct@bf16] value into an f32 value.

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

const fn to_f32_const(self) -> f32

Converts a [struct@bf16] value into an f32 value.

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

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

fn to_f64(self) -> f64

Converts a [struct@bf16] value into an f64 value.

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

const fn to_f64_const(self) -> f64

Converts a [struct@bf16] value into an f64 value.

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

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

const fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

Examples

# use half::prelude::*;

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

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

const fn is_infinite(self) -> bool

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

Examples

# use half::prelude::*;

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());

const fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

Examples

# use half::prelude::*;

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());

const fn is_normal(self) -> bool

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

Examples

# use half::prelude::*;

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());

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;
# use half::prelude::*;

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

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

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

Examples

# use half::prelude::*;

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());

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

# use half::prelude::*;

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());

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

# use half::prelude::*;

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());

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

# use half::prelude::*;
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());

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

# use half::prelude::*;
let x = bf16::from_f32(1.0);
let y = bf16::from_f32(2.0);

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

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

# use half::prelude::*;
let x = bf16::from_f32(1.0);
let y = bf16::from_f32(2.0);

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

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

# use half::prelude::*;
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());

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

# use half::bf16;
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()));

const DIGITS: u32 = 2;

Approximate number of [struct@bf16] significant digits in base 10

const EPSILON: bf16 = _;

[struct@bf16] machine epsilon value

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

const INFINITY: bf16 = _;

[struct@bf16] positive Infinity (+∞)

const MANTISSA_DIGITS: u32 = 8;

Number of [struct@bf16] significant digits in base 2

const MAX: bf16 = _;

Largest finite [struct@bf16] value

const MAX_10_EXP: i32 = 38;

Maximum possible [struct@bf16] power of 10 exponent

const MAX_EXP: i32 = 128;

Maximum possible [struct@bf16] power of 2 exponent

const MIN: bf16 = _;

Smallest finite [struct@bf16] value

const MIN_10_EXP: i32 = -37;

Minimum possible normal [struct@bf16] power of 10 exponent

const MIN_EXP: i32 = -125;

One greater than the minimum possible normal [struct@bf16] power of 2 exponent

const MIN_POSITIVE: bf16 = _;

Smallest positive normal [struct@bf16] value

const NAN: bf16 = _;

[struct@bf16] Not a Number (NaN)

const NEG_INFINITY: bf16 = _;

[struct@bf16] negative infinity (-∞).

const RADIX: u32 = 2;

The radix or base of the internal representation of [struct@bf16]

const MIN_POSITIVE_SUBNORMAL: bf16 = _;

Minimum positive subnormal [struct@bf16] value

const MAX_SUBNORMAL: bf16 = _;

Maximum subnormal [struct@bf16] value

const ONE: bf16 = _;

[struct@bf16] 1

const ZERO: bf16 = _;

[struct@bf16] 0

const NEG_ZERO: bf16 = _;

[struct@bf16] -0

const NEG_ONE: bf16 = _;

[struct@bf16] -1

const E: bf16 = _;

[struct@bf16] Euler's number (ℯ)

const PI: bf16 = _;

[struct@bf16] Archimedes' constant (π)

const FRAC_1_PI: bf16 = _;

[struct@bf16] 1/π

const FRAC_1_SQRT_2: bf16 = _;

[struct@bf16] 1/√2

const FRAC_2_PI: bf16 = _;

[struct@bf16] 2/π

const FRAC_2_SQRT_PI: bf16 = _;

[struct@bf16] 2/√π

const FRAC_PI_2: bf16 = _;

[struct@bf16] π/2

const FRAC_PI_3: bf16 = _;

[struct@bf16] π/3

const FRAC_PI_4: bf16 = _;

[struct@bf16] π/4

const FRAC_PI_6: bf16 = _;

[struct@bf16] π/6

const FRAC_PI_8: bf16 = _;

[struct@bf16] π/8

const LN_10: bf16 = _;

[struct@bf16] 𝗅𝗇 10

const LN_2: bf16 = _;

[struct@bf16] 𝗅𝗇 2

const LOG10_E: bf16 = _;

[struct@bf16] 𝗅𝗈𝗀₁₀ℯ

const LOG10_2: bf16 = _;

[struct@bf16] 𝗅𝗈𝗀₁₀2

const LOG2_E: bf16 = _;

[struct@bf16] 𝗅𝗈𝗀₂ℯ

const LOG2_10: bf16 = _;

[struct@bf16] 𝗅𝗈𝗀₂10

const SQRT_2: bf16 = _;

[struct@bf16] √2