Struct half::f16

source · 
#[repr(transparent)]
pub struct f16(_);
Expand description

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. Because f16 is primarily for efficient storage, floating point operations such as addition, multiplication, etc. are not implemented. Operations should be performed with f32 or higher-precision types and converted to/from f16 as necessary.

Implementations§

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

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

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.

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

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.

Converts a f16 into the underlying bit representation.

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]);

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]);

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]
});

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));

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));

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));

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.

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.

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());

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());

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());

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());

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);

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());

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());

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());

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());

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);

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);

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());

Approximate number of f16 significant digits in base 10

f16 machine epsilon value

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

f16 positive Infinity (+∞)

Number of f16 significant digits in base 2

Largest finite f16 value

Maximum possible f16 power of 10 exponent

Maximum possible f16 power of 2 exponent

Smallest finite f16 value

Minimum possible normal f16 power of 10 exponent

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

Smallest positive normal f16 value

f16 Not a Number (NaN)

f16 negative infinity (-∞)

The radix or base of the internal representation of f16

Minimum positive subnormal f16 value

Maximum subnormal f16 value

f16 1

f16 0

f16 -0

f16 -1

f16 Euler’s number (ℯ)

f16 Archimedes’ constant (π)

f16 1/π

f16 1/√2

f16 2/π

f16 2/√π

f16 π/2

f16 π/3

f16 π/4

f16 π/6

f16 π/8

f16 𝗅𝗇 10

f16 𝗅𝗇 2

f16 𝗅𝗈𝗀₁₀ℯ

f16 𝗅𝗈𝗀₁₀2

f16 𝗅𝗈𝗀₂ℯ

f16 𝗅𝗈𝗀₂10

f16 √2

Trait Implementations§

The resulting type after applying the + operator.
Performs the + operation. Read more
The resulting type after applying the + operator.
Performs the + operation. Read more
The resulting type after applying the + operator.
Performs the + operation. Read more
The resulting type after applying the + operator.
Performs the + operation. Read more
Performs the += operation. Read more
Performs the += operation. Read more
Formats the value using the given formatter.
Returns a copy of the value. Read more
Performs copy-assignment from source. Read more
Formats the value using the given formatter. Read more
Returns the “default value” for a type. Read more
Formats the value using the given formatter. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
The associated error which can be returned from parsing.
Parses a string s to return a value of this type. Read more
Formats the value using the given formatter.
Formats the value using the given formatter.
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
The resulting type after applying the - operator.
Performs the unary - operation. Read more
Formats the value using the given formatter.
This method tests for self and other values to be equal, and is used by ==. Read more
This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
This method returns an ordering between self and other values if one exists. Read more
This method tests less than (for self and other) and is used by the < operator. Read more
This method tests less than or equal to (for self and other) and is used by the <= operator. Read more
This method tests greater than (for self and other) and is used by the > operator. Read more
This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more
Method which takes an iterator and generates Self from the elements by multiplying the items. Read more
Method which takes an iterator and generates Self from the elements by multiplying the items. Read more
The resulting type after applying the % operator.
Performs the % operation. Read more
The resulting type after applying the % operator.
Performs the % operation. Read more
The resulting type after applying the % operator.
Performs the % operation. Read more
The resulting type after applying the % operator.
Performs the % operation. Read more
Performs the %= operation. Read more
Performs the %= operation. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
Performs the -= operation. Read more
Performs the -= operation. Read more
Method which takes an iterator and generates Self from the elements by “summing up” the items. Read more
Method which takes an iterator and generates Self from the elements by “summing up” the items. Read more
Formats the value using the given formatter.
Formats the value using the given formatter.

Auto Trait Implementations§

Blanket Implementations§

Gets the TypeId of self. Read more
Immutably borrows from an owned value. Read more
Mutably borrows from an owned value. Read more

Returns the argument unchanged.

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

The type returned in the event of a conversion error.
Performs the conversion.
The type returned in the event of a conversion error.
Performs the conversion.