Struct gemm_f16::f16

pub struct f16(/* private fields */);

A 16-bit floating point type implementing the IEEE 754-2008 standard binary16 a.k.a “half” format.

This 16-bit floating point type is intended for efficient storage where the full range and precision of a larger floating point value is not required.

Implementations

impl f16

pub const fn from_bits(bits: u16) -> f16

Constructs a 16-bit floating point value from the raw bits.

pub fn from_f32(value: f32) -> f16

Constructs a 16-bit floating point value from a 32-bit floating point value.

This operation is lossy. If the 32-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are preserved. 32-bit subnormal values are too tiny to be represented in 16-bits and result in ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals or ±0. All other values are truncated and rounded to the nearest representable 16-bit value.

pub const fn from_f32_const(value: f32) -> f16

Constructs a 16-bit floating point 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 to large to fit in 16-bits, ±∞ will result. NaN values are preserved. 32-bit subnormal values are too tiny to be represented in 16-bits and result in ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals or ±0. All other values are truncated and rounded to the nearest representable 16-bit value.

pub fn from_f64(value: f64) -> f16

Constructs a 16-bit floating point value from a 64-bit floating point value.

This operation is lossy. If the 64-bit value is to large to fit in 16-bits, ±∞ will result. NaN values are preserved. 64-bit subnormal values are too tiny to be represented in 16-bits and result in ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals or ±0. All other values are truncated and rounded to the nearest representable 16-bit value.

pub const fn from_f64_const(value: f64) -> f16

Constructs a 16-bit floating point 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 in 16-bits, ±∞ will result. NaN values are preserved. 64-bit subnormal values are too tiny to be represented in 16-bits and result in ±0. Exponents that underflow the minimum 16-bit exponent will result in 16-bit subnormals or ±0. All other values are truncated and rounded to the nearest representable 16-bit value.

pub const fn to_bits(self) -> u16

Converts a f16 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 = f16::from_f32(12.5).to_le_bytes();
assert_eq!(bytes, [0x40, 0x4A]);

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 = f16::from_f32(12.5).to_be_bytes();
assert_eq!(bytes, [0x4A, 0x40]);

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 = f16::from_f32(12.5).to_ne_bytes();
assert_eq!(bytes, if cfg!(target_endian = "big") {
    [0x4A, 0x40]
} else {
    [0x40, 0x4A]
});

pub const fn from_le_bytes(bytes: [u8; 2]) -> f16

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

Examples

let value = f16::from_le_bytes([0x40, 0x4A]);
assert_eq!(value, f16::from_f32(12.5));

pub const fn from_be_bytes(bytes: [u8; 2]) -> f16

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

Examples

let value = f16::from_be_bytes([0x4A, 0x40]);
assert_eq!(value, f16::from_f32(12.5));

pub const fn from_ne_bytes(bytes: [u8; 2]) -> f16

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 = f16::from_ne_bytes(if cfg!(target_endian = "big") {
    [0x4A, 0x40]
} else {
    [0x40, 0x4A]
});
assert_eq!(value, f16::from_f32(12.5));

pub fn to_f32(self) -> f32

Converts a f16 value into a f32 value.

This conversion is lossless as all 16-bit floating point values can be represented exactly in 32-bit floating point.

pub const fn to_f32_const(self) -> f32

Converts a f16 value into a 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 16-bit floating point values can be represented exactly in 32-bit floating point.

pub fn to_f64(self) -> f64

Converts a f16 value into a f64 value.

This conversion is lossless as all 16-bit floating point values can be represented exactly in 64-bit floating point.

pub const fn to_f64_const(self) -> f64

Converts a f16 value into a 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 16-bit floating point values can be represented exactly in 64-bit floating point.

pub const fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

Examples

let nan = f16::NAN;
let f = f16::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 = f16::from_f32(7.0f32);
let inf = f16::INFINITY;
let neg_inf = f16::NEG_INFINITY;
let nan = f16::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 = f16::from_f32(7.0f32);
let inf = f16::INFINITY;
let neg_inf = f16::NEG_INFINITY;
let nan = f16::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 = f16::MIN_POSITIVE;
let max = f16::MAX;
let lower_than_min = f16::from_f32(1.0e-10_f32);
let zero = f16::from_f32(0.0_f32);

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

assert!(!zero.is_normal());
assert!(!f16::NAN.is_normal());
assert!(!f16::INFINITY.is_normal());
// Values between `0` and `min` are Subnormal.
assert!(!lower_than_min.is_normal());

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 = f16::from_f32(12.4_f32);
let inf = f16::INFINITY;

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

pub const fn signum(self) -> f16

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
• NAN if the number is NaN

Examples

let f = f16::from_f32(3.5_f32);

assert_eq!(f.signum(), f16::from_f32(1.0));
assert_eq!(f16::NEG_INFINITY.signum(), f16::from_f32(-1.0));

assert!(f16::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 = f16::NAN;
let f = f16::from_f32(7.0_f32);
let g = f16::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 = f16::NAN;
let f = f16::from_f32(7.0f32);
let g = f16::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: f16) -> f16

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 = f16::from_f32(3.5);

assert_eq!(f.copysign(f16::from_f32(0.42)), f16::from_f32(3.5));
assert_eq!(f.copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5));
assert_eq!((-f).copysign(f16::from_f32(0.42)), f16::from_f32(3.5));
assert_eq!((-f).copysign(f16::from_f32(-0.42)), f16::from_f32(-3.5));

assert!(f16::NAN.copysign(f16::from_f32(1.0)).is_nan());

pub fn max(self, other: f16) -> f16

Returns the maximum of the two numbers.

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

Examples

let x = f16::from_f32(1.0);
let y = f16::from_f32(2.0);

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

pub fn min(self, other: f16) -> f16

Returns the minimum of the two numbers.

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

Examples

let x = f16::from_f32(1.0);
let y = f16::from_f32(2.0);

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

pub fn clamp(self, min: f16, max: f16) -> f16

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!(f16::from_f32(-3.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(-2.0));
assert!(f16::from_f32(0.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(0.0));
assert!(f16::from_f32(2.0).clamp(f16::from_f32(-2.0), f16::from_f32(1.0)) == f16::from_f32(1.0));
assert!(f16::NAN.clamp(f16::from_f32(-2.0), f16::from_f32(1.0)).is_nan());

pub fn total_cmp(&self, other: &f16) -> 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 f16. For example, they consider negative and positive zero equal, while total_cmp doesn’t.

The interpretation of the signaling NaN bit follows the definition in the IEEE 754 standard, which may not match the interpretation by some of the older, non-conformant (e.g. MIPS) hardware implementations.

Examples

let mut v: Vec<f16> = vec![];
v.push(f16::ONE);
v.push(f16::INFINITY);
v.push(f16::NEG_INFINITY);
v.push(f16::NAN);
v.push(f16::MAX_SUBNORMAL);
v.push(-f16::MAX_SUBNORMAL);
v.push(f16::ZERO);
v.push(f16::NEG_ZERO);
v.push(f16::NEG_ONE);
v.push(f16::MIN_POSITIVE);

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

assert!(v
    .into_iter()
    .zip(
        [
            f16::NEG_INFINITY,
            f16::NEG_ONE,
            -f16::MAX_SUBNORMAL,
            f16::NEG_ZERO,
            f16::ZERO,
            f16::MAX_SUBNORMAL,
            f16::MIN_POSITIVE,
            f16::ONE,
            f16::INFINITY,
            f16::NAN
        ]
        .iter()
    )
    .all(|(a, b)| a.to_bits() == b.to_bits()));

pub const DIGITS: u32 = 3u32

Approximate number of f16 significant digits in base 10

pub const EPSILON: f16 = _

f16 machine epsilon value

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

pub const INFINITY: f16 = _

f16 positive Infinity (+∞)

pub const MANTISSA_DIGITS: u32 = 11u32

Number of f16 significant digits in base 2

pub const MAX: f16 = _

Largest finite f16 value

pub const MAX_10_EXP: i32 = 4i32

Maximum possible f16 power of 10 exponent

pub const MAX_EXP: i32 = 16i32

Maximum possible f16 power of 2 exponent

pub const MIN: f16 = _

Smallest finite f16 value

pub const MIN_10_EXP: i32 = -4i32

Minimum possible normal f16 power of 10 exponent

pub const MIN_EXP: i32 = -13i32

One greater than the minimum possible normal f16 power of 2 exponent

pub const MIN_POSITIVE: f16 = _

Smallest positive normal f16 value

pub const NAN: f16 = _

f16 Not a Number (NaN)

pub const NEG_INFINITY: f16 = _

f16 negative infinity (-∞)

pub const RADIX: u32 = 2u32

The radix or base of the internal representation of f16

pub const MIN_POSITIVE_SUBNORMAL: f16 = _

Minimum positive subnormal f16 value

pub const MAX_SUBNORMAL: f16 = _

Maximum subnormal f16 value

pub const ONE: f16 = _

f16 1

pub const ZERO: f16 = _

f16 0

pub const NEG_ZERO: f16 = _

f16 -0

pub const NEG_ONE: f16 = _

f16 -1

pub const E: f16 = _

f16 Euler’s number (ℯ)

pub const PI: f16 = _

f16 Archimedes’ constant (π)

pub const FRAC_1_PI: f16 = _

f16 1/π

pub const FRAC_1_SQRT_2: f16 = _

f16 1/√2

pub const FRAC_2_PI: f16 = _

f16 2/π

pub const FRAC_2_SQRT_PI: f16 = _

f16 2/√π

pub const FRAC_PI_2: f16 = _

f16 π/2

pub const FRAC_PI_3: f16 = _

f16 π/3

pub const FRAC_PI_4: f16 = _

f16 π/4

pub const FRAC_PI_6: f16 = _

f16 π/6

pub const FRAC_PI_8: f16 = _

f16 π/8

pub const LN_10: f16 = _

f16 𝗅𝗇 10

pub const LN_2: f16 = _

f16 𝗅𝗇 2

pub const LOG10_E: f16 = _

f16 𝗅𝗈𝗀₁₀ℯ

pub const LOG10_2: f16 = _

f16 𝗅𝗈𝗀₁₀2

pub const LOG2_E: f16 = _

f16 𝗅𝗈𝗀₂ℯ

pub const LOG2_10: f16 = _

f16 𝗅𝗈𝗀₂10

pub const SQRT_2: f16 = _

f16 √2

Trait Implementations

impl Add<&f16> for &f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, rhs: &f16) -> <&f16 as Add<&f16>>::Output

Performs the + operation.

impl Add<&f16> for f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, rhs: &f16) -> <f16 as Add<&f16>>::Output

Performs the + operation.

impl Add<f16> for &f16

type Output = <f16 as Add>::Output

The resulting type after applying the + operator.

fn add(self, rhs: f16) -> <&f16 as Add<f16>>::Output

Performs the + operation.

impl Add for f16

type Output = f16

The resulting type after applying the + operator.

fn add(self, rhs: f16) -> <f16 as Add>::Output

Performs the + operation.

impl AddAssign<&f16> for f16

fn add_assign(&mut self, rhs: &f16)

Performs the += operation.

impl AddAssign for f16

fn add_assign(&mut self, rhs: f16)

Performs the += operation.

impl AsPrimitive<f16> for f16

fn as_(self) -> f16

Convert a value to another, using the as operator.

impl AsPrimitive<f32> for f16

fn as_(self) -> f32

Convert a value to another, using the as operator.

impl AsPrimitive<f64> for f16

fn as_(self) -> f64

Convert a value to another, using the as operator.

impl AsPrimitive<i16> for f16

fn as_(self) -> i16

Convert a value to another, using the as operator.

impl AsPrimitive<i32> for f16

fn as_(self) -> i32

Convert a value to another, using the as operator.

impl AsPrimitive<i64> for f16

fn as_(self) -> i64

Convert a value to another, using the as operator.

impl AsPrimitive<i8> for f16

fn as_(self) -> i8

Convert a value to another, using the as operator.

impl AsPrimitive<isize> for f16

fn as_(self) -> isize

Convert a value to another, using the as operator.

impl AsPrimitive<u16> for f16

fn as_(self) -> u16

Convert a value to another, using the as operator.

impl AsPrimitive<u32> for f16

fn as_(self) -> u32

Convert a value to another, using the as operator.

impl AsPrimitive<u64> for f16

fn as_(self) -> u64

Convert a value to another, using the as operator.

impl AsPrimitive<u8> for f16

fn as_(self) -> u8

Convert a value to another, using the as operator.

impl AsPrimitive<usize> for f16

fn as_(self) -> usize

Convert a value to another, using the as operator.

impl Binary for f16

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

Formats the value using the given formatter.

impl Bounded for f16

fn min_value() -> f16

Returns the smallest finite number this type can represent

fn max_value() -> f16

Returns the largest finite number this type can represent

impl Clone for f16

fn clone(&self) -> f16

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Conj for f16

fn conj(self) -> f16

impl Debug for f16

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

Formats the value using the given formatter.

impl Default for f16

fn default() -> f16

Returns the “default value” for a type.

impl Display for f16

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

Formats the value using the given formatter.

impl Div<&f16> for &f16

type Output = <f16 as Div>::Output

The resulting type after applying the / operator.

fn div(self, rhs: &f16) -> <&f16 as Div<&f16>>::Output

Performs the / operation.

impl Div<&f16> for f16

type Output = <f16 as Div>::Output

The resulting type after applying the / operator.

fn div(self, rhs: &f16) -> <f16 as Div<&f16>>::Output

Performs the / operation.

impl Div<f16> for &f16

type Output = <f16 as Div>::Output

The resulting type after applying the / operator.

fn div(self, rhs: f16) -> <&f16 as Div<f16>>::Output

Performs the / operation.

impl Div for f16

type Output = f16

The resulting type after applying the / operator.

fn div(self, rhs: f16) -> <f16 as Div>::Output

Performs the / operation.

impl DivAssign<&f16> for f16

fn div_assign(&mut self, rhs: &f16)

Performs the /= operation.

impl DivAssign for f16

fn div_assign(&mut self, rhs: f16)

Performs the /= operation.

impl Float for f16

fn nan() -> f16

Returns the NaN value.

fn infinity() -> f16

Returns the infinite value.

fn neg_infinity() -> f16

Returns the negative infinite value.

fn neg_zero() -> f16

Returns -0.0.

fn min_value() -> f16

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> f16

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

fn epsilon() -> f16

Returns epsilon, a small positive value.

fn max_value() -> f16

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) -> f16

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

fn ceil(self) -> f16

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

fn round(self) -> f16

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

fn trunc(self) -> f16

Return the integer part of a number.

fn fract(self) -> f16

Returns the fractional part of a number.

fn abs(self) -> f16

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

fn signum(self) -> f16

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: f16, b: f16) -> f16

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) -> f16

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

fn powi(self, n: i32) -> f16

Raise a number to an integer power.

fn powf(self, n: f16) -> f16

Raise a number to a floating point power.

fn sqrt(self) -> f16

Take the square root of a number.

fn exp(self) -> f16

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

fn exp2(self) -> f16

Returns 2^(self).

fn ln(self) -> f16

Returns the natural logarithm of the number.

fn log(self, base: f16) -> f16

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

fn log2(self) -> f16

Returns the base 2 logarithm of the number.

fn log10(self) -> f16

Returns the base 10 logarithm of the number.

fn to_degrees(self) -> f16

Converts radians to degrees.

fn to_radians(self) -> f16

Converts degrees to radians.

fn max(self, other: f16) -> f16

Returns the maximum of the two numbers.

fn min(self, other: f16) -> f16

Returns the minimum of the two numbers.

fn abs_sub(self, other: f16) -> f16

The positive difference of two numbers.

fn cbrt(self) -> f16

Take the cubic root of a number.

fn hypot(self, other: f16) -> f16

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

fn sin(self) -> f16

Computes the sine of a number (in radians).

fn cos(self) -> f16

Computes the cosine of a number (in radians).

fn tan(self) -> f16

Computes the tangent of a number (in radians).

fn asin(self) -> f16

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) -> f16

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) -> f16

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

fn atan2(self, other: f16) -> f16

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

fn sin_cos(self) -> (f16, f16)

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

fn exp_m1(self) -> f16

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

fn ln_1p(self) -> f16

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

fn sinh(self) -> f16

Hyperbolic sine function.

fn cosh(self) -> f16

Hyperbolic cosine function.

fn tanh(self) -> f16

Hyperbolic tangent function.

fn asinh(self) -> f16

Inverse hyperbolic sine function.

fn acosh(self) -> f16

Inverse hyperbolic cosine function.

fn atanh(self) -> f16

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 copysign(self, sign: Self) -> Self

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

impl FloatConst for f16

fn E() -> f16

Return Euler’s number.

fn FRAC_1_PI() -> f16

Return 1.0 / π.

fn FRAC_1_SQRT_2() -> f16

Return 1.0 / sqrt(2.0).

fn FRAC_2_PI() -> f16

Return 2.0 / π.

fn FRAC_2_SQRT_PI() -> f16

Return 2.0 / sqrt(π).

fn FRAC_PI_2() -> f16

Return π / 2.0.

fn FRAC_PI_3() -> f16

Return π / 3.0.

fn FRAC_PI_4() -> f16

Return π / 4.0.

fn FRAC_PI_6() -> f16

Return π / 6.0.

fn FRAC_PI_8() -> f16

Return π / 8.0.

fn LN_10() -> f16

Return ln(10.0).

fn LN_2() -> f16

Return ln(2.0).

fn LOG10_E() -> f16

Return log10(e).

fn LOG2_E() -> f16

Return log2(e).

fn PI() -> f16

Return Archimedes’ constant π.

fn SQRT_2() -> f16

Return sqrt(2.0).

fn LOG10_2() -> f16

where f16: Sized + Div<Output = f16>,

Return log10(2.0).

fn LOG2_10() -> f16

where f16: Sized + Div<Output = f16>,

Return log2(10.0).

fn TAU() -> Self

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

Return the full circle constant τ.

impl FloatCore for f16

fn infinity() -> f16

Returns positive infinity.

fn neg_infinity() -> f16

Returns negative infinity.

fn nan() -> f16

Returns NaN.

fn neg_zero() -> f16

Returns -0.0.

fn min_value() -> f16

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> f16

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

fn epsilon() -> f16

Returns epsilon, a small positive value.

fn max_value() -> f16

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) -> f16

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

fn ceil(self) -> f16

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

fn round(self) -> f16

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

fn trunc(self) -> f16

Return the integer part of a number.

fn fract(self) -> f16

Returns the fractional part of a number.

fn abs(self) -> f16

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

fn signum(self) -> f16

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: f16) -> f16

Returns the minimum of the two numbers.

fn max(self, other: f16) -> f16

Returns the maximum of the two numbers.

fn recip(self) -> f16

Returns the reciprocal (multiplicative inverse) of the number.

fn powi(self, exp: i32) -> f16

Raise a number to an integer power.

fn to_degrees(self) -> f16

Converts to degrees, assuming the number is in radians.

fn to_radians(self) -> f16

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.

impl From<i8> for f16

fn from(x: i8) -> f16

Converts to this type from the input type.

impl From<u8> for f16

fn from(x: u8) -> f16

Converts to this type from the input type.

impl FromPrimitive for f16

fn from_i64(n: i64) -> Option<f16>

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<f16>

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<f16>

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<f16>

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<f16>

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<f16>

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<f16>

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<f16>

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<f16>

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<f16>

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 f16

type Err = ParseFloatError

The associated error which can be returned from parsing.

fn from_str(src: &str) -> Result<f16, ParseFloatError>

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

impl LowerExp for f16

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

Formats the value using the given formatter.

impl LowerHex for f16

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

Formats the value using the given formatter.

impl Mul<&f16> for &f16

type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, rhs: &f16) -> <&f16 as Mul<&f16>>::Output

Performs the * operation.

impl Mul<&f16> for f16

type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, rhs: &f16) -> <f16 as Mul<&f16>>::Output

Performs the * operation.

impl Mul<f16> for &f16

type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, rhs: f16) -> <&f16 as Mul<f16>>::Output

Performs the * operation.

impl Mul for f16

type Output = f16

The resulting type after applying the * operator.

fn mul(self, rhs: f16) -> <f16 as Mul>::Output

Performs the * operation.

impl MulAssign<&f16> for f16

fn mul_assign(&mut self, rhs: &f16)

Performs the *= operation.

impl MulAssign for f16

fn mul_assign(&mut self, rhs: f16)

Performs the *= operation.

impl Neg for &f16

type Output = <f16 as Neg>::Output

The resulting type after applying the - operator.

fn neg(self) -> <&f16 as Neg>::Output

Performs the unary - operation.

impl Neg for f16

type Output = f16

The resulting type after applying the - operator.

fn neg(self) -> <f16 as Neg>::Output

Performs the unary - operation.

impl Num for f16

type FromStrRadixErr = <f32 as Num>::FromStrRadixErr

fn from_str_radix( str: &str, radix: u32 ) -> Result<f16, <f16 as Num>::FromStrRadixErr>

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

impl NumCast for f16

fn from<T>(n: T) -> Option<f16>

where T: ToPrimitive,

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 f16

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

Formats the value using the given formatter.

impl One for f16

fn one() -> f16

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 f16

fn eq(&self, other: &f16) -> bool

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

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

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

impl PartialOrd for f16

fn partial_cmp(&self, other: &f16) -> Option<Ordering>

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

fn lt(&self, other: &f16) -> bool

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

fn le(&self, other: &f16) -> bool

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

fn gt(&self, other: &f16) -> bool

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

fn ge(&self, other: &f16) -> bool

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

impl<'a> Product<&'a f16> for f16

fn product<I>(iter: I) -> f16

where I: Iterator<Item = &'a f16>,

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

impl Product for f16

fn product<I>(iter: I) -> f16

where I: Iterator<Item = f16>,

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

impl Rem<&f16> for &f16

type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, rhs: &f16) -> <&f16 as Rem<&f16>>::Output

Performs the % operation.

impl Rem<&f16> for f16

type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, rhs: &f16) -> <f16 as Rem<&f16>>::Output

Performs the % operation.

impl Rem<f16> for &f16

type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, rhs: f16) -> <&f16 as Rem<f16>>::Output

Performs the % operation.

impl Rem for f16

type Output = f16

The resulting type after applying the % operator.

fn rem(self, rhs: f16) -> <f16 as Rem>::Output

Performs the % operation.

impl RemAssign<&f16> for f16

fn rem_assign(&mut self, rhs: &f16)

Performs the %= operation.

impl RemAssign for f16

fn rem_assign(&mut self, rhs: f16)

Performs the %= operation.

impl Sub<&f16> for &f16

type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, rhs: &f16) -> <&f16 as Sub<&f16>>::Output

Performs the - operation.

impl Sub<&f16> for f16

type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, rhs: &f16) -> <f16 as Sub<&f16>>::Output

Performs the - operation.

impl Sub<f16> for &f16

type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, rhs: f16) -> <&f16 as Sub<f16>>::Output

Performs the - operation.

impl Sub for f16

type Output = f16

The resulting type after applying the - operator.

fn sub(self, rhs: f16) -> <f16 as Sub>::Output

Performs the - operation.

impl SubAssign<&f16> for f16

fn sub_assign(&mut self, rhs: &f16)

Performs the -= operation.

impl SubAssign for f16

fn sub_assign(&mut self, rhs: f16)

Performs the -= operation.

impl<'a> Sum<&'a f16> for f16

fn sum<I>(iter: I) -> f16

where I: Iterator<Item = &'a f16>,

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

impl Sum for f16

fn sum<I>(iter: I) -> f16

where I: Iterator<Item = f16>,

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

impl ToPrimitive for f16

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 f16

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

Formats the value using the given formatter.

impl UpperHex for f16

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

Formats the value using the given formatter.

impl Zero for f16

fn zero() -> f16

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 Zeroable for f16

fn zeroed() -> Self

Calls zeroed.

impl Copy for f16

impl Pod for f16