Struct image2::f16

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

16-bit float 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

16-bit float

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 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.

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.

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.

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 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.

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.

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.

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());

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()));

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.

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

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 !=.

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

Min value

Max value

I/O base type

Convert to f64

Convert from f64

Returns true when T is a floating point type

Get the type name

Set a value from an f64 value

Set a value from normalized float

Convert from T to normalized float

Convert to T from normalized float

Scale a value to fit between 0 and 1.0 based on the min/max values for T

Scale an f64 value to fit the range supported by T

Ensure the given value is less than the max allowed and greater than or equal to the minimum value Read more

Convert a value from one type to another

Get the number of bits for a data type

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 alignment of pointer.

The type for initializers.

Initializes a with the given initializer. Read more

Dereferences the given pointer. Read more

Mutably dereferences the given pointer. Read more

Drops the object pointed to by the given pointer. Read more

The resulting type after obtaining ownership.

Creates owned data from borrowed data, usually by cloning. Read more

Uses borrowed data to replace owned data, usually by cloning. Read more

Converts the given value to a String. Read more

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.