Primitive Type f16

🔬This is a nightly-only experimental API. (f16 #116909)
Expand description

A 16-bit floating point type (specifically, the “binary16” type defined in IEEE 754-2008).

This type is very similar to f32 but has decreased precision because it uses half as many bits. Please see [the documentation for f32 or Wikipedia on half-precision values for more information.

Note that most common platforms will not support f16 in hardware without enabling extra target features, with the notable exception of Apple Silicon (also known as M1, M2, etc.) processors. Hardware support on x86-64 requires the avx512fp16 feature, while RISC-V requires Zhf. Usually the fallback implementation will be to use f32 hardware if it exists, and convert between f16 and f32 when performing math.

See also the std::f16::consts module.

Implementations§

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impl f16

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pub const RADIX: u32 = 2u32

🔬This is a nightly-only experimental API. (f16 #116909)

The radix or base of the internal representation of f16.

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pub const MANTISSA_DIGITS: u32 = 11u32

🔬This is a nightly-only experimental API. (f16 #116909)

Number of significant digits in base 2.

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pub const DIGITS: u32 = 3u32

🔬This is a nightly-only experimental API. (f16 #116909)

Approximate number of significant digits in base 10.

This is the maximum x such that any decimal number with x significant digits can be converted to f16 and back without loss.

Equal to floor(log10 2MANTISSA_DIGITS − 1).

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pub const EPSILON: f16 = {transmute(0x1400): f16}

🔬This is a nightly-only experimental API. (f16 #116909)

Machine epsilon value for f16.

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

Equal to 21 − MANTISSA_DIGITS.

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pub const MIN: f16 = {transmute(0xfbff): f16}

🔬This is a nightly-only experimental API. (f16 #116909)

Smallest finite f16 value.

Equal to −MAX.

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pub const MIN_POSITIVE: f16 = {transmute(0x0400): f16}

🔬This is a nightly-only experimental API. (f16 #116909)

Smallest positive normal f16 value.

Equal to 2MIN_EXP − 1.

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pub const MAX: f16 = {transmute(0x7bff): f16}

🔬This is a nightly-only experimental API. (f16 #116909)

Largest finite f16 value.

Equal to (1 − 2MANTISSA_DIGITS) 2MAX_EXP.

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pub const MIN_EXP: i32 = -13i32

🔬This is a nightly-only experimental API. (f16 #116909)

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

If x = MIN_EXP, then normal numbers ≥ 0.5 × 2x.

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pub const MAX_EXP: i32 = 16i32

🔬This is a nightly-only experimental API. (f16 #116909)

Maximum possible power of 2 exponent.

If x = MAX_EXP, then normal numbers < 1 × 2x.

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pub const MIN_10_EXP: i32 = -4i32

🔬This is a nightly-only experimental API. (f16 #116909)

Minimum x for which 10x is normal.

Equal to ceil(log10 MIN_POSITIVE).

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pub const MAX_10_EXP: i32 = 4i32

🔬This is a nightly-only experimental API. (f16 #116909)

Maximum x for which 10x is normal.

Equal to floor(log10 MAX).

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pub const fn is_nan(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if this value is NaN.

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pub fn is_sign_positive(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if self has a positive sign, including +0.0, NaNs with positive sign bit and positive infinity. Note that IEEE 754 doesn’t assign any meaning to the sign bit in case of a NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the result of is_sign_positive on a NaN might produce an unexpected result in some cases. See explanation of NaN as a special value for more info.

#![feature(f16)]

let f = 7.0_f16;
let g = -7.0_f16;

assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());
Run
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pub fn is_sign_negative(self) -> bool

🔬This is a nightly-only experimental API. (f16 #116909)

Returns true if self has a negative sign, including -0.0, NaNs with negative sign bit and negative infinity. Note that IEEE 754 doesn’t assign any meaning to the sign bit in case of a NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the result of is_sign_negative on a NaN might produce an unexpected result in some cases. See explanation of NaN as a special value for more info.

#![feature(f16)]

let f = 7.0_f16;
let g = -7.0_f16;

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());
Run
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pub fn to_bits(self) -> u16

🔬This is a nightly-only experimental API. (f16 #116909)

Raw transmutation to u16.

This is currently identical to transmute::<f16, u16>(self) on all platforms.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Note that this function is distinct from as casting, which attempts to preserve the numeric value, and not the bitwise value.

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pub fn from_bits(v: u16) -> Self

🔬This is a nightly-only experimental API. (f16 #116909)

Raw transmutation from u16.

This is currently identical to transmute::<u16, f16>(v) on all platforms. It turns out this is incredibly portable, for two reasons:

  • Floats and Ints have the same endianness on all supported platforms.
  • IEEE 754 very precisely specifies the bit layout of floats.

However there is one caveat: prior to the 2008 version of IEEE 754, how to interpret the NaN signaling bit wasn’t actually specified. Most platforms (notably x86 and ARM) picked the interpretation that was ultimately standardized in 2008, but some didn’t (notably MIPS). As a result, all signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.

Rather than trying to preserve signaling-ness cross-platform, this implementation favors preserving the exact bits. This means that any payloads encoded in NaNs will be preserved even if the result of this method is sent over the network from an x86 machine to a MIPS one.

If the results of this method are only manipulated by the same architecture that produced them, then there is no portability concern.

If the input isn’t NaN, then there is no portability concern.

If you don’t care about signalingness (very likely), then there is no portability concern.

Note that this function is distinct from as casting, which attempts to preserve the numeric value, and not the bitwise value.

Trait Implementations§

1.0.0 · source§

impl Add<&f16> for &f16

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type Output = <f16 as Add>::Output

The resulting type after applying the + operator.
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fn add(self, other: &f16) -> <f16 as Add<f16>>::Output

Performs the + operation. Read more
1.0.0 · source§

impl Add<&f16> for f16

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type Output = <f16 as Add>::Output

The resulting type after applying the + operator.
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fn add(self, other: &f16) -> <f16 as Add<f16>>::Output

Performs the + operation. Read more
1.0.0 · source§

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

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type Output = <f16 as Add>::Output

The resulting type after applying the + operator.
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fn add(self, other: f16) -> <f16 as Add<f16>>::Output

Performs the + operation. Read more
1.0.0 (const: unstable) · source§

impl Add for f16

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type Output = f16

The resulting type after applying the + operator.
const: unstable · source§

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

Performs the + operation. Read more
1.22.0 · source§

impl AddAssign<&f16> for f16

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

Performs the += operation. Read more
1.8.0 · source§

impl AddAssign for f16

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fn add_assign(&mut self, other: f16)

Performs the += operation. Read more
1.0.0 · source§

impl Clone for f16

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fn clone(&self) -> Self

Returns a copy of the value. Read more
1.0.0 · source§

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

Performs copy-assignment from source. Read more
1.0.0 · source§

impl Debug for f16

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

Formats the value using the given formatter. Read more
1.0.0 · source§

impl Default for f16

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fn default() -> f16

Returns the default value of 0.0

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impl Div<&f16> for &f16

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type Output = <f16 as Div>::Output

The resulting type after applying the / operator.
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fn div(self, other: &f16) -> <f16 as Div<f16>>::Output

Performs the / operation. Read more
1.0.0 · source§

impl Div<&f16> for f16

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type Output = <f16 as Div>::Output

The resulting type after applying the / operator.
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fn div(self, other: &f16) -> <f16 as Div<f16>>::Output

Performs the / operation. Read more
1.0.0 · source§

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

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type Output = <f16 as Div>::Output

The resulting type after applying the / operator.
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fn div(self, other: f16) -> <f16 as Div<f16>>::Output

Performs the / operation. Read more
1.0.0 · source§

impl Div for f16

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type Output = f16

The resulting type after applying the / operator.
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fn div(self, other: f16) -> f16

Performs the / operation. Read more
1.22.0 · source§

impl DivAssign<&f16> for f16

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

Performs the /= operation. Read more
1.8.0 · source§

impl DivAssign for f16

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fn div_assign(&mut self, other: f16)

Performs the /= operation. Read more
1.6.0 · source§

impl From<f16> for f128

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fn from(small: f16) -> Self

Converts f16 to f128 losslessly.

1.6.0 · source§

impl From<f16> for f64

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fn from(small: f16) -> Self

Converts f16 to f64 losslessly.

1.0.0 · source§

impl Mul<&f16> for &f16

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type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.
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fn mul(self, other: &f16) -> <f16 as Mul<f16>>::Output

Performs the * operation. Read more
1.0.0 · source§

impl Mul<&f16> for f16

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type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.
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fn mul(self, other: &f16) -> <f16 as Mul<f16>>::Output

Performs the * operation. Read more
1.0.0 · source§

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

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type Output = <f16 as Mul>::Output

The resulting type after applying the * operator.
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fn mul(self, other: f16) -> <f16 as Mul<f16>>::Output

Performs the * operation. Read more
1.0.0 · source§

impl Mul for f16

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type Output = f16

The resulting type after applying the * operator.
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fn mul(self, other: f16) -> f16

Performs the * operation. Read more
1.22.0 · source§

impl MulAssign<&f16> for f16

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

Performs the *= operation. Read more
1.8.0 · source§

impl MulAssign for f16

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fn mul_assign(&mut self, other: f16)

Performs the *= operation. Read more
1.0.0 · source§

impl Neg for &f16

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type Output = <f16 as Neg>::Output

The resulting type after applying the - operator.
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fn neg(self) -> <f16 as Neg>::Output

Performs the unary - operation. Read more
1.0.0 · source§

impl Neg for f16

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type Output = f16

The resulting type after applying the - operator.
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fn neg(self) -> f16

Performs the unary - operation. Read more
1.0.0 (const: unstable) · source§

impl PartialEq for f16

const: unstable · source§

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

This method tests for self and other values to be equal, and is used by ==.
const: unstable · source§

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

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

impl PartialOrd for f16

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

This method returns an ordering between self and other values if one exists. Read more
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fn lt(&self, other: &f16) -> bool

This method tests less than (for self and other) and is used by the < operator. Read more
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fn le(&self, other: &f16) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more
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fn ge(&self, other: &f16) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more
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fn gt(&self, other: &f16) -> bool

This method tests greater than (for self and other) and is used by the > operator. Read more
1.0.0 · source§

impl Rem<&f16> for &f16

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type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.
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fn rem(self, other: &f16) -> <f16 as Rem<f16>>::Output

Performs the % operation. Read more
1.0.0 · source§

impl Rem<&f16> for f16

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type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.
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fn rem(self, other: &f16) -> <f16 as Rem<f16>>::Output

Performs the % operation. Read more
1.0.0 · source§

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

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type Output = <f16 as Rem>::Output

The resulting type after applying the % operator.
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fn rem(self, other: f16) -> <f16 as Rem<f16>>::Output

Performs the % operation. Read more
1.0.0 · source§

impl Rem for f16

The remainder from the division of two floats.

The remainder has the same sign as the dividend and is computed as: x - (x / y).trunc() * y.

§Examples

let x: f32 = 50.50;
let y: f32 = 8.125;
let remainder = x - (x / y).trunc() * y;

// The answer to both operations is 1.75
assert_eq!(x % y, remainder);
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type Output = f16

The resulting type after applying the % operator.
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fn rem(self, other: f16) -> f16

Performs the % operation. Read more
1.22.0 · source§

impl RemAssign<&f16> for f16

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

Performs the %= operation. Read more
1.8.0 · source§

impl RemAssign for f16

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fn rem_assign(&mut self, other: f16)

Performs the %= operation. Read more
1.0.0 · source§

impl Sub<&f16> for &f16

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type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.
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fn sub(self, other: &f16) -> <f16 as Sub<f16>>::Output

Performs the - operation. Read more
1.0.0 · source§

impl Sub<&f16> for f16

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type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.
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fn sub(self, other: &f16) -> <f16 as Sub<f16>>::Output

Performs the - operation. Read more
1.0.0 · source§

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

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type Output = <f16 as Sub>::Output

The resulting type after applying the - operator.
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fn sub(self, other: f16) -> <f16 as Sub<f16>>::Output

Performs the - operation. Read more
1.0.0 · source§

impl Sub for f16

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type Output = f16

The resulting type after applying the - operator.
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fn sub(self, other: f16) -> f16

Performs the - operation. Read more
1.22.0 · source§

impl SubAssign<&f16> for f16

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

Performs the -= operation. Read more
1.8.0 · source§

impl SubAssign for f16

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fn sub_assign(&mut self, other: f16)

Performs the -= operation. Read more
1.0.0 · source§

impl Copy for f16

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impl FloatToInt<i128> for f16

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impl FloatToInt<i16> for f16

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impl FloatToInt<i32> for f16

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impl FloatToInt<i64> for f16

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impl FloatToInt<i8> for f16

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impl FloatToInt<isize> for f16

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impl FloatToInt<u128> for f16

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impl FloatToInt<u16> for f16

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impl FloatToInt<u32> for f16

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impl FloatToInt<u64> for f16

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impl FloatToInt<u8> for f16

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impl FloatToInt<usize> for f16

Auto Trait Implementations§

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impl Freeze for f16

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impl RefUnwindSafe for f16

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impl Send for f16

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impl Sync for f16

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impl Unpin for f16

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impl UnwindSafe for f16

Blanket Implementations§

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

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

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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.