Struct bf16

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

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 struct@f16. While struct@f16 has a precision of 11 bits, bf16 has a precision of only 8 bits.

Implementations

impl bf16

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

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.

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.

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.

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.

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.

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()));

Trait Implementations

impl Add<&bf16> for &bf16

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

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add 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 for bf16

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl AsPrimitive<bf16> for bf16

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for f16

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for f32

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for f64

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for i16

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for i32

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for i64

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for i8

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for isize

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for u16

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for u32

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for u64

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for u8

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<bf16> for usize

fn as_(self) -> bf16

Convert a value to another, using the as operator.

impl AsPrimitive<f16> for bf16

fn as_(self) -> f16

Convert a value to another, using the as operator.

impl AsPrimitive<f32> for bf16

fn as_(self) -> f32

Convert a value to another, using the as operator.

impl AsPrimitive<f64> for bf16

fn as_(self) -> f64

Convert a value to another, using the as operator.

impl AsPrimitive<i16> for bf16

fn as_(self) -> i16

Convert a value to another, using the as operator.

impl AsPrimitive<i32> for bf16

fn as_(self) -> i32

Convert a value to another, using the as operator.

impl AsPrimitive<i64> for bf16

fn as_(self) -> i64

Convert a value to another, using the as operator.

impl AsPrimitive<i8> for bf16

fn as_(self) -> i8

Convert a value to another, using the as operator.

impl AsPrimitive<isize> for bf16

fn as_(self) -> isize

Convert a value to another, using the as operator.

impl AsPrimitive<u16> for bf16

fn as_(self) -> u16

Convert a value to another, using the as operator.

impl AsPrimitive<u32> for bf16

fn as_(self) -> u32

Convert a value to another, using the as operator.

impl AsPrimitive<u64> for bf16

fn as_(self) -> u64

Convert a value to another, using the as operator.

impl AsPrimitive<u8> for bf16

fn as_(self) -> u8

Convert a value to another, using the as operator.

impl AsPrimitive<usize> for bf16

fn as_(self) -> usize

Convert a value to another, using the as operator.

impl Binary for bf16

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

Formats the value using the given formatter.

impl Bounded for bf16

fn min_value() -> Self

Returns the smallest finite number this type can represent

fn max_value() -> Self

Returns the largest finite number this type can represent

impl Clone for bf16

fn clone(&self) -> bf16

Returns a duplicate 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>::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>::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>::Output

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div 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 for bf16

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl Float for bf16

fn nan() -> Self

Returns the NaN value.

fn infinity() -> Self

Returns the infinite value.

fn neg_infinity() -> Self

Returns the negative infinite value.

fn neg_zero() -> Self

Returns -0.0.

fn min_value() -> Self

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> Self

Returns the smallest positive, normalized value that this type can represent.

fn epsilon() -> Self

Returns epsilon, a small positive value.

fn max_value() -> Self

Returns the largest finite value that this type can represent.

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

fn is_infinite(self) -> bool

Returns true if this value is positive infinity or negative infinity and false otherwise.

fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

fn is_normal(self) -> bool

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

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.

fn floor(self) -> Self

Returns the largest integer less than or equal to a number.

fn ceil(self) -> Self

Returns the smallest integer greater than or equal to a number.

fn round(self) -> Self

Returns the nearest integer to a number. Round half-way cases away from 0.0.

fn trunc(self) -> Self

Return the integer part of a number.

fn fract(self) -> Self

Returns the fractional part of a number.

fn abs(self) -> Self

Computes the absolute value of self. Returns Float::nan() if the number is Float::nan().

fn signum(self) -> Self

Returns a number that represents the sign of self.

fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0, Float::infinity(), and Float::nan().

fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0, Float::neg_infinity(), and -Float::nan().

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.

fn recip(self) -> Self

Take the reciprocal (inverse) of a number, 1/x.

fn powi(self, n: i32) -> Self

Raise a number to an integer power.

fn powf(self, n: Self) -> Self

Raise a number to a floating point power.

fn sqrt(self) -> Self

Take the square root of a number.

fn exp(self) -> Self

Returns e^(self), (the exponential function).

fn exp2(self) -> Self

Returns 2^(self).

fn ln(self) -> Self

Returns the natural logarithm of the number.

fn log(self, base: Self) -> Self

Returns the logarithm of the number with respect to an arbitrary base.

fn log2(self) -> Self

Returns the base 2 logarithm of the number.

fn log10(self) -> Self

Returns the base 10 logarithm of the number.

fn to_degrees(self) -> Self

Converts radians to degrees.

fn to_radians(self) -> Self

Converts degrees to radians.

fn max(self, other: Self) -> Self

Returns the maximum of the two numbers.

fn min(self, other: Self) -> Self

Returns the minimum of the two numbers.

fn abs_sub(self, other: Self) -> Self

The positive difference of two numbers.

fn cbrt(self) -> Self

Take the cubic root of a number.

fn hypot(self, other: Self) -> Self

Calculate the length of the hypotenuse of a right-angle triangle given legs of length x and y.

fn sin(self) -> Self

Computes the sine of a number (in radians).

fn cos(self) -> Self

Computes the cosine of a number (in radians).

fn tan(self) -> Self

Computes the tangent of a number (in radians).

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].

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].

fn atan(self) -> Self

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

fn atan2(self, other: Self) -> Self

Computes the four quadrant arctangent of self (y) and other (x).

fn sin_cos(self) -> (Self, Self)

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)).

fn exp_m1(self) -> Self

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero.

fn ln_1p(self) -> Self

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately.

fn sinh(self) -> Self

Hyperbolic sine function.

fn cosh(self) -> Self

Hyperbolic cosine function.

fn tanh(self) -> Self

Hyperbolic tangent function.

fn asinh(self) -> Self

Inverse hyperbolic sine function.

fn acosh(self) -> Self

Inverse hyperbolic cosine function.

fn atanh(self) -> Self

Inverse hyperbolic tangent function.

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.

fn is_subnormal(self) -> bool

Returns true if the number is subnormal.

fn clamp(self, min: Self, max: Self) -> Self

Clamps a value between a min and max.

fn copysign(self, sign: Self) -> Self

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

impl FloatConst for bf16

fn E() -> Self

Return Euler’s number.

fn FRAC_1_PI() -> Self

Return 1.0 / π.

fn FRAC_1_SQRT_2() -> Self

Return 1.0 / sqrt(2.0).

fn FRAC_2_PI() -> Self

Return 2.0 / π.

fn FRAC_2_SQRT_PI() -> Self

Return 2.0 / sqrt(π).

fn FRAC_PI_2() -> Self

Return π / 2.0.

fn FRAC_PI_3() -> Self

Return π / 3.0.

fn FRAC_PI_4() -> Self

Return π / 4.0.

fn FRAC_PI_6() -> Self

Return π / 6.0.

fn FRAC_PI_8() -> Self

Return π / 8.0.

fn LN_10() -> Self

Return ln(10.0).

fn LN_2() -> Self

Return ln(2.0).

fn LOG10_E() -> Self

Return log10(e).

fn LOG2_E() -> Self

Return log2(e).

fn PI() -> Self

Return Archimedes’ constant π.

fn SQRT_2() -> Self

Return sqrt(2.0).

fn LOG10_2() -> Self

where Self: Sized + Div<Self, Output = Self>,

Return log10(2.0).

fn LOG2_10() -> Self

where Self: Sized + Div<Self, Output = Self>,

Return log2(10.0).

fn TAU() -> Self

where Self: Sized + Add<Output = Self>,

Return the full circle constant τ.

impl FloatCore for bf16

fn infinity() -> Self

Returns positive infinity.

fn neg_infinity() -> Self

Returns negative infinity.

fn nan() -> Self

Returns NaN.

fn neg_zero() -> Self

Returns -0.0.

fn min_value() -> Self

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> Self

Returns the smallest positive, normalized value that this type can represent.

fn epsilon() -> Self

Returns epsilon, a small positive value.

fn max_value() -> Self

Returns the largest finite value that this type can represent.

fn is_nan(self) -> bool

Returns true if the number is NaN.

fn is_infinite(self) -> bool

Returns true if the number is infinite.

fn is_finite(self) -> bool

Returns true if the number is neither infinite or NaN.

fn is_normal(self) -> bool

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

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.

fn floor(self) -> Self

Returns the largest integer less than or equal to a number.

fn ceil(self) -> Self

Returns the smallest integer greater than or equal to a number.

fn round(self) -> Self

Returns the nearest integer to a number. Round half-way cases away from 0.0.

fn trunc(self) -> Self

Return the integer part of a number.

fn fract(self) -> Self

Returns the fractional part of a number.

fn abs(self) -> Self

Computes the absolute value of self. Returns FloatCore::nan() if the number is FloatCore::nan().

fn signum(self) -> Self

Returns a number that represents the sign of self.

fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0 and FloatCore::infinity(), and FloatCore::nan().

fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0 and FloatCore::neg_infinity(), and -FloatCore::nan().

fn min(self, other: Self) -> Self

Returns the minimum of the two numbers.

fn max(self, other: Self) -> Self

Returns the maximum of the two numbers.

fn recip(self) -> Self

Returns the reciprocal (multiplicative inverse) of the number.

fn powi(self, exp: i32) -> Self

Raise a number to an integer power.

fn to_degrees(self) -> Self

Converts to degrees, assuming the number is in radians.

fn to_radians(self) -> Self

Converts to radians, assuming the number is in degrees.

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.

fn is_subnormal(self) -> bool

Returns true if the number is subnormal.

fn clamp(self, min: Self, max: Self) -> Self

A value bounded by a minimum and a maximum

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 FromBytes for bf16

type Bytes = [u8; 2]

fn from_be_bytes(bytes: &Self::Bytes) -> Self

Create a number from its representation as a byte array in big endian.

fn from_le_bytes(bytes: &Self::Bytes) -> Self

Create a number from its representation as a byte array in little endian.

fn from_ne_bytes(bytes: &Self::Bytes) -> Self

Create a number from its memory representation as a byte array in native endianness.

impl FromPrimitive for bf16

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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>::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>::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>::Output

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul 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 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 Num for bf16

type FromStrRadixErr = <f32 as Num>::FromStrRadixErr

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

Convert from a string and radix (typically 2..=36).

impl NumCast for bf16

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.

impl Octal for bf16

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

Formats the value using the given formatter.

impl One for bf16

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl PartialEq for bf16

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl PartialOrd 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

Tests less than (for self and other) and is used by the < operator.

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

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

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

Tests greater than (for self and other) and is used by the > operator.

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

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

Takes an iterator and generates Self from the elements by multiplying the items.

impl Product for bf16

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

Takes an iterator and generates Self from the elements by multiplying the items.

impl Rem<&bf16> for &bf16

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

The resulting type after applying the % operator.

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

Performs the % operation.

impl Rem 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 for bf16

fn rem_assign(&mut self, rhs: Self)

Performs the %= operation.

impl Sub<&bf16> for &bf16

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

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub 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 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

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

impl Sum for bf16

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

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

impl ToBytes for bf16

type Bytes = [u8; 2]

fn to_be_bytes(&self) -> Self::Bytes

Return the memory representation of this number as a byte array in big-endian byte order.

fn to_le_bytes(&self) -> Self::Bytes

Return the memory representation of this number as a byte array in little-endian byte order.

fn to_ne_bytes(&self) -> Self::Bytes

Return the memory representation of this number as a byte array in native byte order.

impl ToPrimitive for bf16

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 Zero for bf16

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl Copy for bf16