#[repr(C)]
pub struct DualQuaternion<T> { pub real: Quaternion<T>, pub dual: Quaternion<T>, }
Expand description

A dual quaternion.

§Indexing

DualQuaternions are stored as [..real, ..dual]. Both of the quaternion components are laid out in i, j, k, w order.

§Example


let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);

let dq = DualQuaternion::from_real_and_dual(real, dual);
assert_eq!(dq[0], 2.0);
assert_eq!(dq[1], 3.0);

assert_eq!(dq[4], 6.0);
assert_eq!(dq[7], 5.0);

NOTE: As of December 2020, dual quaternion support is a work in progress. If a feature that you need is missing, feel free to open an issue or a PR. See https://github.com/dimforge/nalgebra/issues/487

Fields§

§real: Quaternion<T>

The real component of the quaternion

§dual: Quaternion<T>

The dual component of the quaternion

Implementations§

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impl<T> DualQuaternion<T>

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pub fn normalize(&self) -> DualQuaternion<T>

Normalizes this quaternion.

§Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq = DualQuaternion::from_real_and_dual(real, dual);

let dq_normalized = dq.normalize();

relative_eq!(dq_normalized.real.norm(), 1.0);
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pub fn normalize_mut(&mut self) -> T

Normalizes this quaternion.

§Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let mut dq = DualQuaternion::from_real_and_dual(real, dual);

dq.normalize_mut();

relative_eq!(dq.real.norm(), 1.0);
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pub fn conjugate(&self) -> DualQuaternion<T>

The conjugate of this dual quaternion, containing the conjugate of the real and imaginary parts..

§Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq = DualQuaternion::from_real_and_dual(real, dual);

let conj = dq.conjugate();
assert!(conj.real.i == -2.0 && conj.real.j == -3.0 && conj.real.k == -4.0);
assert!(conj.real.w == 1.0);
assert!(conj.dual.i == -6.0 && conj.dual.j == -7.0 && conj.dual.k == -8.0);
assert!(conj.dual.w == 5.0);
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pub fn conjugate_mut(&mut self)

Replaces this quaternion by its conjugate.

§Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let mut dq = DualQuaternion::from_real_and_dual(real, dual);

dq.conjugate_mut();
assert!(dq.real.i == -2.0 && dq.real.j == -3.0 && dq.real.k == -4.0);
assert!(dq.real.w == 1.0);
assert!(dq.dual.i == -6.0 && dq.dual.j == -7.0 && dq.dual.k == -8.0);
assert!(dq.dual.w == 5.0);
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pub fn try_inverse(&self) -> Option<DualQuaternion<T>>
where T: RealField,

Inverts this dual quaternion if it is not zero.

§Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq = DualQuaternion::from_real_and_dual(real, dual);
let inverse = dq.try_inverse();

assert!(inverse.is_some());
assert_relative_eq!(inverse.unwrap() * dq, DualQuaternion::identity());

//Non-invertible case
let zero = Quaternion::new(0.0, 0.0, 0.0, 0.0);
let dq = DualQuaternion::from_real_and_dual(zero, zero);
let inverse = dq.try_inverse();

assert!(inverse.is_none());
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pub fn try_inverse_mut(&mut self) -> bool
where T: RealField,

Inverts this dual quaternion in-place if it is not zero.

§Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq = DualQuaternion::from_real_and_dual(real, dual);
let mut dq_inverse = dq;
dq_inverse.try_inverse_mut();

assert_relative_eq!(dq_inverse * dq, DualQuaternion::identity());

//Non-invertible case
let zero = Quaternion::new(0.0, 0.0, 0.0, 0.0);
let mut dq = DualQuaternion::from_real_and_dual(zero, zero);
assert!(!dq.try_inverse_mut());
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pub fn lerp(&self, other: &DualQuaternion<T>, t: T) -> DualQuaternion<T>

Linear interpolation between two dual quaternions.

Computes self * (1 - t) + other * t.

§Example
let dq1 = DualQuaternion::from_real_and_dual(
    Quaternion::new(1.0, 0.0, 0.0, 4.0),
    Quaternion::new(0.0, 2.0, 0.0, 0.0)
);
let dq2 = DualQuaternion::from_real_and_dual(
    Quaternion::new(2.0, 0.0, 1.0, 0.0),
    Quaternion::new(0.0, 2.0, 0.0, 0.0)
);
assert_eq!(dq1.lerp(&dq2, 0.25), DualQuaternion::from_real_and_dual(
    Quaternion::new(1.25, 0.0, 0.25, 3.0),
    Quaternion::new(0.0, 2.0, 0.0, 0.0)
));
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impl<T> DualQuaternion<T>
where T: Scalar,

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pub fn from_real_and_dual( real: Quaternion<T>, dual: Quaternion<T>, ) -> DualQuaternion<T>

Creates a dual quaternion from its rotation and translation components.

§Example
let rot = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let trans = Quaternion::new(5.0, 6.0, 7.0, 8.0);

let dq = DualQuaternion::from_real_and_dual(rot, trans);
assert_eq!(dq.real.w, 1.0);
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pub fn identity() -> DualQuaternion<T>
where T: SimdRealField,

The dual quaternion multiplicative identity.

§Example

let dq1 = DualQuaternion::identity();
let dq2 = DualQuaternion::from_real_and_dual(
    Quaternion::new(1.,2.,3.,4.),
    Quaternion::new(5.,6.,7.,8.)
);

assert_eq!(dq1 * dq2, dq2);
assert_eq!(dq2 * dq1, dq2);
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pub fn cast<To>(self) -> DualQuaternion<To>
where To: Scalar, DualQuaternion<To>: SupersetOf<DualQuaternion<T>>,

Cast the components of self to another type.

§Example
let q = DualQuaternion::from_real(Quaternion::new(1.0f64, 2.0, 3.0, 4.0));
let q2 = q.cast::<f32>();
assert_eq!(q2, DualQuaternion::from_real(Quaternion::new(1.0f32, 2.0, 3.0, 4.0)));
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impl<T> DualQuaternion<T>

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pub fn from_real(real: Quaternion<T>) -> DualQuaternion<T>

Creates a dual quaternion from only its real part, with no translation component.

§Example
let rot = Quaternion::new(1.0, 2.0, 3.0, 4.0);

let dq = DualQuaternion::from_real(rot);
assert_eq!(dq.real.w, 1.0);
assert_eq!(dq.dual.w, 0.0);

Trait Implementations§

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impl<T> AbsDiffEq for DualQuaternion<T>
where T: RealField<Epsilon = T> + AbsDiffEq,

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type Epsilon = T

Used for specifying relative comparisons.
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fn default_epsilon() -> <DualQuaternion<T> as AbsDiffEq>::Epsilon

The default tolerance to use when testing values that are close together. Read more
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fn abs_diff_eq( &self, other: &DualQuaternion<T>, epsilon: <DualQuaternion<T> as AbsDiffEq>::Epsilon, ) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.
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fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of [AbsDiffEq::abs_diff_eq].
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impl<'a, 'b, T> Add<&'b DualQuaternion<T>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the + operator.
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fn add( self, rhs: &'b DualQuaternion<T>, ) -> <&'a DualQuaternion<T> as Add<&'b DualQuaternion<T>>>::Output

Performs the + operation. Read more
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impl<'b, T> Add<&'b DualQuaternion<T>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the + operator.
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fn add( self, rhs: &'b DualQuaternion<T>, ) -> <DualQuaternion<T> as Add<&'b DualQuaternion<T>>>::Output

Performs the + operation. Read more
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impl<'a, T> Add<DualQuaternion<T>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the + operator.
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fn add( self, rhs: DualQuaternion<T>, ) -> <&'a DualQuaternion<T> as Add<DualQuaternion<T>>>::Output

Performs the + operation. Read more
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impl<T> Add for DualQuaternion<T>

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type Output = DualQuaternion<T>

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

Performs the + operation. Read more
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impl<'b, T> AddAssign<&'b DualQuaternion<T>> for DualQuaternion<T>

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fn add_assign(&mut self, rhs: &'b DualQuaternion<T>)

Performs the += operation. Read more
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impl<T> AddAssign for DualQuaternion<T>

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fn add_assign(&mut self, rhs: DualQuaternion<T>)

Performs the += operation. Read more
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impl<T> AsMut<[T; 8]> for DualQuaternion<T>
where T: SimdRealField,

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fn as_mut(&mut self) -> &mut [T; 8]

Converts this type into a mutable reference of the (usually inferred) input type.
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impl<T> AsRef<[T; 8]> for DualQuaternion<T>
where T: SimdRealField,

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fn as_ref(&self) -> &[T; 8]

Converts this type into a shared reference of the (usually inferred) input type.
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impl<T> Clone for DualQuaternion<T>
where T: Clone,

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fn clone(&self) -> DualQuaternion<T>

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<T> Debug for DualQuaternion<T>
where T: Debug,

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

Formats the value using the given formatter. Read more
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impl<T> Default for DualQuaternion<T>
where T: Scalar + Zero,

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fn default() -> DualQuaternion<T>

Returns the “default value” for a type. Read more
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impl<'a, 'b, T> Div<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the / operator.
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fn div( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <&'a DualQuaternion<T> as Div<&'b Unit<DualQuaternion<T>>>>::Output

Performs the / operation. Read more
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impl<'b, T> Div<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the / operator.
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fn div( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <DualQuaternion<T> as Div<&'b Unit<DualQuaternion<T>>>>::Output

Performs the / operation. Read more
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impl<'a, T> Div<T> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the / operator.
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fn div(self, n: T) -> <&'a DualQuaternion<T> as Div<T>>::Output

Performs the / operation. Read more
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impl<T> Div<T> for DualQuaternion<T>

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type Output = DualQuaternion<T>

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

Performs the / operation. Read more
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impl<'a, T> Div<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the / operator.
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fn div( self, rhs: Unit<DualQuaternion<T>>, ) -> <&'a DualQuaternion<T> as Div<Unit<DualQuaternion<T>>>>::Output

Performs the / operation. Read more
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impl<T> Div<Unit<DualQuaternion<T>>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the / operator.
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fn div( self, rhs: Unit<DualQuaternion<T>>, ) -> <DualQuaternion<T> as Div<Unit<DualQuaternion<T>>>>::Output

Performs the / operation. Read more
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impl<'b, T> DivAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

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fn div_assign(&mut self, rhs: &'b Unit<DualQuaternion<T>>)

Performs the /= operation. Read more
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impl<T> DivAssign<T> for DualQuaternion<T>

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fn div_assign(&mut self, n: T)

Performs the /= operation. Read more
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impl<T> DivAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>

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fn div_assign(&mut self, rhs: Unit<DualQuaternion<T>>)

Performs the /= operation. Read more
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impl<T> Index<usize> for DualQuaternion<T>
where T: SimdRealField,

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type Output = T

The returned type after indexing.
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fn index(&self, i: usize) -> &<DualQuaternion<T> as Index<usize>>::Output

Performs the indexing (container[index]) operation. Read more
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impl<T> IndexMut<usize> for DualQuaternion<T>
where T: SimdRealField,

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fn index_mut(&mut self, i: usize) -> &mut T

Performs the mutable indexing (container[index]) operation. Read more
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impl<'a, 'b, T> Mul<&'b DualQuaternion<T>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: &'b DualQuaternion<T>, ) -> <&'a DualQuaternion<T> as Mul<&'b DualQuaternion<T>>>::Output

Performs the * operation. Read more
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impl<'a, 'b, T> Mul<&'b DualQuaternion<T>> for &'a Unit<DualQuaternion<T>>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: &'b DualQuaternion<T>, ) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b DualQuaternion<T>>>::Output

Performs the * operation. Read more
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impl<'b, T> Mul<&'b DualQuaternion<T>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: &'b DualQuaternion<T>, ) -> <DualQuaternion<T> as Mul<&'b DualQuaternion<T>>>::Output

Performs the * operation. Read more
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impl<'b, T> Mul<&'b DualQuaternion<T>> for Unit<DualQuaternion<T>>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: &'b DualQuaternion<T>, ) -> <Unit<DualQuaternion<T>> as Mul<&'b DualQuaternion<T>>>::Output

Performs the * operation. Read more
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impl<'a, 'b, T> Mul<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <&'a DualQuaternion<T> as Mul<&'b Unit<DualQuaternion<T>>>>::Output

Performs the * operation. Read more
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impl<'b, T> Mul<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <DualQuaternion<T> as Mul<&'b Unit<DualQuaternion<T>>>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<DualQuaternion<T>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: DualQuaternion<T>, ) -> <&'a DualQuaternion<T> as Mul<DualQuaternion<T>>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<DualQuaternion<T>> for &'a Unit<DualQuaternion<T>>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: DualQuaternion<T>, ) -> <&'a Unit<DualQuaternion<T>> as Mul<DualQuaternion<T>>>::Output

Performs the * operation. Read more
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impl<T> Mul<DualQuaternion<T>> for Unit<DualQuaternion<T>>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: DualQuaternion<T>, ) -> <Unit<DualQuaternion<T>> as Mul<DualQuaternion<T>>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<T> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul(self, n: T) -> <&'a DualQuaternion<T> as Mul<T>>::Output

Performs the * operation. Read more
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impl<T> Mul<T> for DualQuaternion<T>

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type Output = DualQuaternion<T>

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

Performs the * operation. Read more
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impl<'a, T> Mul<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: Unit<DualQuaternion<T>>, ) -> <&'a DualQuaternion<T> as Mul<Unit<DualQuaternion<T>>>>::Output

Performs the * operation. Read more
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impl<T> Mul<Unit<DualQuaternion<T>>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul( self, rhs: Unit<DualQuaternion<T>>, ) -> <DualQuaternion<T> as Mul<Unit<DualQuaternion<T>>>>::Output

Performs the * operation. Read more
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impl<T> Mul for DualQuaternion<T>

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type Output = DualQuaternion<T>

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

Performs the * operation. Read more
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impl<'b, T> MulAssign<&'b DualQuaternion<T>> for DualQuaternion<T>

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fn mul_assign(&mut self, rhs: &'b DualQuaternion<T>)

Performs the *= operation. Read more
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impl<'b, T> MulAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

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fn mul_assign(&mut self, rhs: &'b Unit<DualQuaternion<T>>)

Performs the *= operation. Read more
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impl<T> MulAssign<T> for DualQuaternion<T>

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fn mul_assign(&mut self, n: T)

Performs the *= operation. Read more
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impl<T> MulAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>

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fn mul_assign(&mut self, rhs: Unit<DualQuaternion<T>>)

Performs the *= operation. Read more
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impl<T> MulAssign for DualQuaternion<T>

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fn mul_assign(&mut self, rhs: DualQuaternion<T>)

Performs the *= operation. Read more
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impl<'a, T> Neg for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the - operator.
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fn neg(self) -> <&'a DualQuaternion<T> as Neg>::Output

Performs the unary - operation. Read more
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impl<T> Neg for DualQuaternion<T>

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type Output = DualQuaternion<T>

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

Performs the unary - operation. Read more
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impl<T> Normed for DualQuaternion<T>
where T: SimdRealField,

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type Norm = <T as SimdComplexField>::SimdRealField

The type of the norm.
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fn norm(&self) -> <T as SimdComplexField>::SimdRealField

Computes the norm.
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fn norm_squared(&self) -> <T as SimdComplexField>::SimdRealField

Computes the squared norm.
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fn scale_mut(&mut self, n: <DualQuaternion<T> as Normed>::Norm)

Multiply self by n.
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fn unscale_mut(&mut self, n: <DualQuaternion<T> as Normed>::Norm)

Divides self by n.
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impl<T> One for DualQuaternion<T>

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fn one() -> DualQuaternion<T>

Returns the multiplicative identity element of Self, 1. Read more
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fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.
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fn is_one(&self) -> bool
where Self: PartialEq,

Returns true if self is equal to the multiplicative identity. Read more
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impl<T> PartialEq for DualQuaternion<T>
where T: Scalar,

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fn eq(&self, right: &DualQuaternion<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.
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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.
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impl<T> RelativeEq for DualQuaternion<T>
where T: RealField<Epsilon = T> + RelativeEq,

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fn default_max_relative() -> <DualQuaternion<T> as AbsDiffEq>::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
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fn relative_eq( &self, other: &DualQuaternion<T>, epsilon: <DualQuaternion<T> as AbsDiffEq>::Epsilon, max_relative: <DualQuaternion<T> as AbsDiffEq>::Epsilon, ) -> bool

A test for equality that uses a relative comparison if the values are far apart.
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fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

The inverse of [RelativeEq::relative_eq].
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impl<'a, 'b, T> Sub<&'b DualQuaternion<T>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the - operator.
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fn sub( self, rhs: &'b DualQuaternion<T>, ) -> <&'a DualQuaternion<T> as Sub<&'b DualQuaternion<T>>>::Output

Performs the - operation. Read more
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impl<'b, T> Sub<&'b DualQuaternion<T>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the - operator.
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fn sub( self, rhs: &'b DualQuaternion<T>, ) -> <DualQuaternion<T> as Sub<&'b DualQuaternion<T>>>::Output

Performs the - operation. Read more
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impl<'a, T> Sub<DualQuaternion<T>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the - operator.
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fn sub( self, rhs: DualQuaternion<T>, ) -> <&'a DualQuaternion<T> as Sub<DualQuaternion<T>>>::Output

Performs the - operation. Read more
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impl<T> Sub for DualQuaternion<T>

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type Output = DualQuaternion<T>

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

Performs the - operation. Read more
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impl<'b, T> SubAssign<&'b DualQuaternion<T>> for DualQuaternion<T>

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fn sub_assign(&mut self, rhs: &'b DualQuaternion<T>)

Performs the -= operation. Read more
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impl<T> SubAssign for DualQuaternion<T>

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fn sub_assign(&mut self, rhs: DualQuaternion<T>)

Performs the -= operation. Read more
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impl<T1, T2> SubsetOf<DualQuaternion<T2>> for DualQuaternion<T1>
where T1: SimdRealField, T2: SimdRealField + SupersetOf<T1>,

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fn to_superset(&self) -> DualQuaternion<T2>

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(dq: &DualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(dq: &DualQuaternion<T2>) -> DualQuaternion<T1>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T> UlpsEq for DualQuaternion<T>
where T: RealField<Epsilon = T> + UlpsEq,

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fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
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fn ulps_eq( &self, other: &DualQuaternion<T>, epsilon: <DualQuaternion<T> as AbsDiffEq>::Epsilon, max_ulps: u32, ) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.
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fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of [UlpsEq::ulps_eq].
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impl<T> Zero for DualQuaternion<T>

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fn zero() -> DualQuaternion<T>

Returns the additive identity element of Self, 0. Read more
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fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.
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fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.
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impl<T> Copy for DualQuaternion<T>
where T: Copy,

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impl<T> Eq for DualQuaternion<T>
where T: Scalar + Eq,

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impl<T> Freeze for DualQuaternion<T>
where T: Freeze,

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impl<T> RefUnwindSafe for DualQuaternion<T>
where T: RefUnwindSafe,

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impl<T> Send for DualQuaternion<T>
where T: Send,

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impl<T> Sync for DualQuaternion<T>
where T: Sync,

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impl<T> Unpin for DualQuaternion<T>
where T: Unpin,

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impl<T> UnwindSafe for DualQuaternion<T>
where T: UnwindSafe,

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impl<T> Any for T
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fn type_id(&self) -> TypeId

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fn equals(&self, other: &(dyn Any + 'static)) -> bool

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fn as_any(&self) -> &(dyn Any + 'static)

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impl<T, U> AsBindGroupShaderType<U> for T
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fn as_bind_group_shader_type(&self, _images: &RenderAssets<Image>) -> U

Return the T [ShaderType] for self. When used in [AsBindGroup] derives, it is safe to assume that all images in self exist.
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where T: 'a,

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fn explicit(self, class: Class, tag: u32) -> TaggedParser<'a, Explicit, Self, E>

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impl<'a, T, E> AsTaggedImplicit<'a, E> for T
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fn implicit( self, class: Class, constructed: bool, tag: u32, ) -> TaggedParser<'a, Implicit, Self, E>

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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
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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> CloneToUninit for T
where T: Copy,

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unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. Read more
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impl<T> CloneToUninit for T
where T: Clone,

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default unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. Read more
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impl<T> Conv for T

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fn conv<T>(self) -> T
where Self: Into<T>,

Converts self into T using Into<T>. Read more
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impl<T> Downcast<T> for T

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fn downcast(&self) -> &T

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impl<T> Downcast for T
where T: Any,

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fn into_any(self: Box<T>) -> Box<dyn Any>

Convert Box<dyn Trait> (where Trait: Downcast) to Box<dyn Any>. Box<dyn Any> can then be further downcast into Box<ConcreteType> where ConcreteType implements Trait.
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fn into_any_rc(self: Rc<T>) -> Rc<dyn Any>

Convert Rc<Trait> (where Trait: Downcast) to Rc<Any>. Rc<Any> can then be further downcast into Rc<ConcreteType> where ConcreteType implements Trait.
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fn as_any(&self) -> &(dyn Any + 'static)

Convert &Trait (where Trait: Downcast) to &Any. This is needed since Rust cannot generate &Any’s vtable from &Trait’s.
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Convert &mut Trait (where Trait: Downcast) to &Any. This is needed since Rust cannot generate &mut Any’s vtable from &mut Trait’s.
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Convert Arc<Trait> (where Trait: Downcast) to Arc<Any>. Arc<Any> can then be further downcast into Arc<ConcreteType> where ConcreteType implements Trait.
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fn as_any(&self) -> &(dyn Any + 'static)

Casts the type to dyn Any.
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This method tests for self and other values to be equal. Read more
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fn equivalent(&self, key: &K) -> bool

Checks if this value is equivalent to the given key. Read more
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fn equivalent(&self, key: &K) -> bool

Compare self to key and return true if they are equal.
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impl<Q, K> Equivalent<K> for Q
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fn equivalent(&self, key: &K) -> bool

Compare self to key and return true if they are equal.
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impl<Q, K> Equivalent<K> for Q
where Q: Eq + ?Sized, K: Borrow<Q> + ?Sized,

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fn equivalent(&self, key: &K) -> bool

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impl<T> FmtForward for T

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fn fmt_binary(self) -> FmtBinary<Self>
where Self: Binary,

Causes self to use its Binary implementation when Debug-formatted.
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fn fmt_display(self) -> FmtDisplay<Self>
where Self: Display,

Causes self to use its Display implementation when Debug-formatted.
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fn fmt_lower_exp(self) -> FmtLowerExp<Self>
where Self: LowerExp,

Causes self to use its LowerExp implementation when Debug-formatted.
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fn fmt_lower_hex(self) -> FmtLowerHex<Self>
where Self: LowerHex,

Causes self to use its LowerHex implementation when Debug-formatted.
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fn fmt_octal(self) -> FmtOctal<Self>
where Self: Octal,

Causes self to use its Octal implementation when Debug-formatted.
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fn fmt_pointer(self) -> FmtPointer<Self>
where Self: Pointer,

Causes self to use its Pointer implementation when Debug-formatted.
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fn fmt_upper_exp(self) -> FmtUpperExp<Self>
where Self: UpperExp,

Causes self to use its UpperExp implementation when Debug-formatted.
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fn fmt_upper_hex(self) -> FmtUpperHex<Self>
where Self: UpperHex,

Causes self to use its UpperHex implementation when Debug-formatted.
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fn fmt_list(self) -> FmtList<Self>
where &'a Self: for<'a> IntoIterator,

Formats each item in a sequence. 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<S> FromSample<S> for S

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fn from_sample_(s: S) -> S

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impl<T> FromWorld for T
where T: Default,

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fn from_world(_world: &mut World) -> T

Creates Self using data from the given [World]
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impl<T> FromWorld for T
where T: Default,

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fn from_world(_world: &World) -> T

Creates Self using data from the given World.
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impl<T> Instrument for T

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fn instrument(self, span: Span) -> Instrumented<Self>

Instruments this type with the provided [Span], returning an Instrumented wrapper. Read more
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fn in_current_span(self) -> Instrumented<Self>

Instruments this type with the current Span, returning an Instrumented wrapper. Read more
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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> IntoEither for T

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fn into_either(self, into_left: bool) -> Either<Self, Self>

Converts self into a Left variant of Either<Self, Self> if into_left is true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
where F: FnOnce(&Self) -> bool,

Converts self into a Left variant of Either<Self, Self> if into_left(&self) returns true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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impl<F, T> IntoSample<T> for F
where T: FromSample<F>,

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fn into_sample(self) -> T

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impl<T> One for T
where T: One,

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fn one() -> T

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impl<T> Pipe for T
where T: ?Sized,

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fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> R
where Self: Sized,

Pipes by value. This is generally the method you want to use. Read more
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fn pipe_ref<'a, R>(&'a self, func: impl FnOnce(&'a Self) -> R) -> R
where R: 'a,

Borrows self and passes that borrow into the pipe function. Read more
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fn pipe_ref_mut<'a, R>(&'a mut self, func: impl FnOnce(&'a mut Self) -> R) -> R
where R: 'a,

Mutably borrows self and passes that borrow into the pipe function. Read more
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fn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> R
where Self: Borrow<B>, B: 'a + ?Sized, R: 'a,

Borrows self, then passes self.borrow() into the pipe function. Read more
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fn pipe_borrow_mut<'a, B, R>( &'a mut self, func: impl FnOnce(&'a mut B) -> R, ) -> R
where Self: BorrowMut<B>, B: 'a + ?Sized, R: 'a,

Mutably borrows self, then passes self.borrow_mut() into the pipe function. Read more
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fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> R
where Self: AsRef<U>, U: 'a + ?Sized, R: 'a,

Borrows self, then passes self.as_ref() into the pipe function.
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fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> R
where Self: AsMut<U>, U: 'a + ?Sized, R: 'a,

Mutably borrows self, then passes self.as_mut() into the pipe function.
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fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> R
where Self: Deref<Target = T>, T: 'a + ?Sized, R: 'a,

Borrows self, then passes self.deref() into the pipe function.
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fn pipe_deref_mut<'a, T, R>( &'a mut self, func: impl FnOnce(&'a mut T) -> R, ) -> R
where Self: DerefMut<Target = T> + Deref, T: 'a + ?Sized, R: 'a,

Mutably borrows self, then passes self.deref_mut() into the pipe function.
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impl<T> Pointable for T

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const ALIGN: usize = _

The alignment of pointer.
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type Init = T

The type for initializers.
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unsafe fn init(init: <T as Pointable>::Init) -> usize

Initializes a with the given initializer. Read more
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unsafe fn deref<'a>(ptr: usize) -> &'a T

Dereferences the given pointer. Read more
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unsafe fn deref_mut<'a>(ptr: usize) -> &'a mut T

Mutably dereferences the given pointer. Read more
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unsafe fn drop(ptr: usize)

Drops the object pointed to by the given pointer. Read more
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impl<T> RawClone for T
where T: Clone,

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unsafe fn raw_clone(src: *const c_void, dst: *mut c_void)

Write the default value of the type to the pointer. Read more
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fn raw_clone_cb() -> Unsafe<&'static (dyn Fn(*const c_void, *mut c_void) + Send + Sync)>

Get a callback suitable for [SchemaData].
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where T: Default,

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unsafe fn raw_default(dst: *mut c_void)

Write the default value of the type to the pointer. Read more
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fn raw_default_cb() -> Unsafe<&'static (dyn Fn(*mut c_void) + Send + Sync)>

Get a callback suitable for [SchemaData].
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unsafe fn raw_drop(ptr: *mut c_void)

Write the default value of the type to the pointer. Read more
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fn raw_drop_cb() -> Unsafe<&'static (dyn Fn(*mut c_void) + Send + Sync)>

Get a callback suitable for [SchemaData].
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impl<T> RawEq for T
where T: Eq,

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unsafe fn raw_eq(a: *const c_void, b: *const c_void) -> bool

Get the hash of the type. Read more
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fn raw_eq_cb() -> Unsafe<&'static (dyn Fn(*const c_void, *const c_void) -> bool + Send + Sync)>

Get a callback suitable for [SchemaData].
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impl<T> Same for T

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type Output = T

Should always be Self
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impl<'gc, T> Singleton<'gc> for T
where T: Default,

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fn create(_: Context<'gc>) -> T

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impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

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fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).
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fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.
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fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.
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impl<T> Tap for T

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fn tap(self, func: impl FnOnce(&Self)) -> Self

Immutable access to a value. Read more
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fn tap_mut(self, func: impl FnOnce(&mut Self)) -> Self

Mutable access to a value. Read more
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fn tap_borrow<B>(self, func: impl FnOnce(&B)) -> Self
where Self: Borrow<B>, B: ?Sized,

Immutable access to the Borrow<B> of a value. Read more
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fn tap_borrow_mut<B>(self, func: impl FnOnce(&mut B)) -> Self
where Self: BorrowMut<B>, B: ?Sized,

Mutable access to the BorrowMut<B> of a value. Read more
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fn tap_ref<R>(self, func: impl FnOnce(&R)) -> Self
where Self: AsRef<R>, R: ?Sized,

Immutable access to the AsRef<R> view of a value. Read more
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fn tap_ref_mut<R>(self, func: impl FnOnce(&mut R)) -> Self
where Self: AsMut<R>, R: ?Sized,

Mutable access to the AsMut<R> view of a value. Read more
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fn tap_deref<T>(self, func: impl FnOnce(&T)) -> Self
where Self: Deref<Target = T>, T: ?Sized,

Immutable access to the Deref::Target of a value. Read more
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fn tap_deref_mut<T>(self, func: impl FnOnce(&mut T)) -> Self
where Self: DerefMut<Target = T> + Deref, T: ?Sized,

Mutable access to the Deref::Target of a value. Read more
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fn tap_dbg(self, func: impl FnOnce(&Self)) -> Self

Calls .tap() only in debug builds, and is erased in release builds.
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fn tap_mut_dbg(self, func: impl FnOnce(&mut Self)) -> Self

Calls .tap_mut() only in debug builds, and is erased in release builds.
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fn tap_borrow_dbg<B>(self, func: impl FnOnce(&B)) -> Self
where Self: Borrow<B>, B: ?Sized,

Calls .tap_borrow() only in debug builds, and is erased in release builds.
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fn tap_borrow_mut_dbg<B>(self, func: impl FnOnce(&mut B)) -> Self
where Self: BorrowMut<B>, B: ?Sized,

Calls .tap_borrow_mut() only in debug builds, and is erased in release builds.
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fn tap_ref_dbg<R>(self, func: impl FnOnce(&R)) -> Self
where Self: AsRef<R>, R: ?Sized,

Calls .tap_ref() only in debug builds, and is erased in release builds.
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fn tap_ref_mut_dbg<R>(self, func: impl FnOnce(&mut R)) -> Self
where Self: AsMut<R>, R: ?Sized,

Calls .tap_ref_mut() only in debug builds, and is erased in release builds.
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fn tap_deref_dbg<T>(self, func: impl FnOnce(&T)) -> Self
where Self: Deref<Target = T>, T: ?Sized,

Calls .tap_deref() only in debug builds, and is erased in release builds.
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fn tap_deref_mut_dbg<T>(self, func: impl FnOnce(&mut T)) -> Self
where Self: DerefMut<Target = T> + Deref, T: ?Sized,

Calls .tap_deref_mut() only in debug builds, and is erased in release builds.
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T, U> ToSample<U> for T
where U: FromSample<T>,

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fn to_sample_(self) -> U

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impl<T> TryConv for T

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fn try_conv<T>(self) -> Result<T, Self::Error>
where Self: TryInto<T>,

Attempts to convert self into T using TryInto<T>. Read more
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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.
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impl<T> TypeData for T
where T: 'static + Send + Sync + Clone,

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fn clone_type_data(&self) -> Box<dyn TypeData>

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impl<T> Upcast<T> for T

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fn upcast(&self) -> Option<&T>

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impl<V, T> VZip<V> for T
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fn vzip(self) -> V

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impl<T> WithSubscriber for T

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fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self>
where S: Into<Dispatch>,

Attaches the provided Subscriber to this type, returning a [WithDispatch] wrapper. Read more
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fn with_current_subscriber(self) -> WithDispatch<Self>

Attaches the current default Subscriber to this type, returning a [WithDispatch] wrapper. Read more
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impl<T> Zero for T
where T: Zero,

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fn zero() -> T

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impl<T, Right> ClosedAdd<Right> for T
where T: Add<Right, Output = T> + AddAssign<Right>,

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impl<T, Right> ClosedDiv<Right> for T
where T: Div<Right, Output = T> + DivAssign<Right>,

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impl<T, Right> ClosedMul<Right> for T
where T: Mul<Right, Output = T> + MulAssign<Right>,

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impl<T> ClosedNeg for T
where T: Neg<Output = T>,

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where T: 'static + Clone + PartialEq + Debug,

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impl<T> SerializableAny for T
where T: 'static + Any + Clone + for<'a> Send + Sync,