math_utils

Struct LinearIso

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pub struct LinearIso<S, V, W, M>(/* private fields */);
Expand description

Invertible linear map

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impl<S, V, W, M> LinearIso<S, V, W, M>
where M: LinearMap<S, V, W> + Copy, V: Module<S>, W: Module<S>, S: Ring,

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pub fn is_invertible(linear_map: M) -> bool

Checks whether the determinant is non-zero

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pub fn is_invertible_approx(linear_map: M) -> bool
where S: RelativeEq<Epsilon = S>,

Checks whether the determinant is non-zero with approximate equality

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pub fn new(linear_map: M) -> Option<Self>

Checks if map is invertible

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pub fn new_approx(linear_map: M) -> Option<Self>
where S: RelativeEq<Epsilon = S>,

Checks if map is invertible with approximate equality

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impl<S: Clone, V: Clone, W: Clone, M: Clone> Clone for LinearIso<S, V, W, M>

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fn clone(&self) -> LinearIso<S, V, W, M>

Returns a duplicate 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<S: Debug, V: Debug, W: Debug, M: Debug> Debug for LinearIso<S, V, W, M>

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

Formats the value using the given formatter. Read more
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impl<S: Default, V: Default, W: Default, M: Default> Default for LinearIso<S, V, W, M>

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fn default() -> LinearIso<S, V, W, M>

Returns the “default value” for a type. Read more
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impl<S, V, W, M> Deref for LinearIso<S, V, W, M>
where M: LinearMap<S, V, W>, V: Module<S>, W: Module<S>, S: Ring,

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type Target = M

The resulting type after dereferencing.
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fn deref(&self) -> &Self::Target

Dereferences the value.
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impl<S, V, W, M> Display for LinearIso<S, V, W, M>
where M: Display,

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

Formats the value using the given formatter. Read more
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impl<S, V> Div for LinearIso<S, V, V, Matrix2<S>>
where V: Module<S, LinearEndo = Matrix2<S>>, S: Ring + Float,

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type Output = LinearIso<S, V, V, Mat2<S>>

The resulting type after applying the / operator.
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fn div(self, rhs: Self) -> Self::Output

Performs the / operation. Read more
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impl<S, V> Div for LinearIso<S, V, V, Matrix3<S>>
where V: Module<S, LinearEndo = Matrix3<S>>, S: Ring + Float,

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type Output = LinearIso<S, V, V, Mat3<S>>

The resulting type after applying the / operator.
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fn div(self, rhs: Self) -> Self::Output

Performs the / operation. Read more
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impl<S, V> Div for LinearIso<S, V, V, Matrix4<S>>
where V: Module<S, LinearEndo = Matrix4<S>>, S: Ring + Float,

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type Output = LinearIso<S, V, V, Mat4<S>>

The resulting type after applying the / operator.
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fn div(self, rhs: Self) -> Self::Output

Performs the / operation. Read more
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impl<S, V> DivAssign for LinearIso<S, V, V, Matrix2<S>>
where V: Module<S, LinearEndo = Matrix2<S>>, S: Ring + Float,

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fn div_assign(&mut self, rhs: Self)

Performs the /= operation. Read more
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impl<S, V> DivAssign for LinearIso<S, V, V, Matrix3<S>>
where V: Module<S, LinearEndo = Matrix3<S>>, S: Ring + Float,

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fn div_assign(&mut self, rhs: Self)

Performs the /= operation. Read more
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impl<S, V> DivAssign for LinearIso<S, V, V, Matrix4<S>>
where V: Module<S, LinearEndo = Matrix4<S>>, S: Ring + Float,

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fn div_assign(&mut self, rhs: Self)

Performs the /= operation. Read more
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impl<S, V> From<LinearIso<S, V, V, <V as Module<S>>::LinearEndo>> for LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes, S: Ring,

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fn from(value: LinearIso<S, V, V, V::LinearEndo>) -> Self

Converts to this type from the input type.
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impl<S, V, W> Inv for LinearIso<S, V, W, Matrix2<S>>
where V: Module<S>, W: Module<S>, S: Ring + Float,

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type Output = LinearIso<S, W, V, Mat2<S>>

The result after applying the operator.
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fn inv(self) -> Self::Output

Returns the multiplicative inverse of self. Read more
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impl<S, V, W> Inv for LinearIso<S, V, W, Matrix3<S>>
where V: Module<S>, W: Module<S>, S: Ring + Float,

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type Output = LinearIso<S, W, V, Mat3<S>>

The result after applying the operator.
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fn inv(self) -> Self::Output

Returns the multiplicative inverse of self. Read more
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impl<S, V, W> Inv for LinearIso<S, V, W, Matrix4<S>>
where V: Module<S>, W: Module<S>, S: Ring + Float,

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type Output = LinearIso<S, W, V, Mat4<S>>

The result after applying the operator.
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fn inv(self) -> Self::Output

Returns the multiplicative inverse of self. Read more
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impl<S> Mul<LinearIso<S, Vec2<S>, Vec2<S>, Mat2<S>>> for Vector2<S>
where S: Ring + MaybeSerDes,

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type Output = Vec2<S>

The resulting type after applying the * operator.
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fn mul(self, rhs: LinearIso<S, Self, Self, Matrix2<S>>) -> Self::Output

Performs the * operation. Read more
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impl<S> Mul<LinearIso<S, Vec3<S>, Vec3<S>, Mat3<S>>> for Vector3<S>
where S: Ring + MaybeSerDes,

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type Output = Vec3<S>

The resulting type after applying the * operator.
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fn mul(self, rhs: LinearIso<S, Self, Self, Matrix3<S>>) -> Self::Output

Performs the * operation. Read more
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impl<S> Mul<LinearIso<S, Vec4<S>, Vec4<S>, Mat4<S>>> for Vector4<S>
where S: Ring + MaybeSerDes,

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type Output = Vec4<S>

The resulting type after applying the * operator.
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fn mul(self, rhs: LinearIso<S, Self, Self, Matrix4<S>>) -> Self::Output

Performs the * operation. Read more
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impl<S, V, W, M> Mul<V> for LinearIso<S, V, W, M>
where M: LinearMap<S, V, W>, V: Module<S>, W: Module<S>, S: Ring,

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type Output = W

The resulting type after applying the * operator.
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fn mul(self, rhs: V) -> Self::Output

Performs the * operation. Read more
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impl<S, V> Mul for LinearIso<S, V, V, V::LinearEndo>
where V: Module<S>, S: Ring,

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type Output = LinearIso<S, V, V, <V as Module<S>>::LinearEndo>

The resulting type after applying the * operator.
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fn mul(self, rhs: Self) -> Self::Output

Performs the * operation. Read more
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impl<S, V> MulAssign for LinearIso<S, V, V, V::LinearEndo>
where V: Module<S>, S: Ring,

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fn mul_assign(&mut self, rhs: Self)

Performs the *= operation. Read more
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impl<S, V> One for LinearIso<S, V, V, V::LinearEndo>
where V: Module<S>, S: Ring,

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fn one() -> Self

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<S: PartialEq, V: PartialEq, W: PartialEq, M: PartialEq> PartialEq for LinearIso<S, V, W, M>

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fn eq(&self, other: &LinearIso<S, V, W, M>) -> bool

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<S: Copy, V: Copy, W: Copy, M: Copy> Copy for LinearIso<S, V, W, M>

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impl<S, V, W, M> StructuralPartialEq for LinearIso<S, V, W, M>

Auto Trait Implementations§

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impl<S, V, W, M> Freeze for LinearIso<S, V, W, M>
where M: Freeze,

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impl<S, V, W, M> RefUnwindSafe for LinearIso<S, V, W, M>
where M: RefUnwindSafe, S: RefUnwindSafe, V: RefUnwindSafe, W: RefUnwindSafe,

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impl<S, V, W, M> Send for LinearIso<S, V, W, M>
where M: Send, S: Send, V: Send, W: Send,

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impl<S, V, W, M> Sync for LinearIso<S, V, W, M>
where M: Sync, S: Sync, V: Sync, W: Sync,

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impl<S, V, W, M> Unpin for LinearIso<S, V, W, M>
where M: Unpin, S: Unpin, V: Unpin, W: Unpin,

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impl<S, V, W, M> UnwindSafe for LinearIso<S, V, W, M>
where M: UnwindSafe, S: UnwindSafe, V: UnwindSafe, W: UnwindSafe,

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> Az for T

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fn az<Dst>(self) -> Dst
where T: Cast<Dst>,

Casts the value.
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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<Src, Dst> CastFrom<Src> for Dst
where Src: Cast<Dst>,

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fn cast_from(src: Src) -> Dst

Casts the value.
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impl<T> CheckedAs for T

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fn checked_as<Dst>(self) -> Option<Dst>
where T: CheckedCast<Dst>,

Casts the value.
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impl<Src, Dst> CheckedCastFrom<Src> for Dst
where Src: CheckedCast<Dst>,

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fn checked_cast_from(src: Src) -> Option<Dst>

Casts the value.
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. 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> 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<Src, Dst> LosslessTryInto<Dst> for Src
where Dst: LosslessTryFrom<Src>,

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fn lossless_try_into(self) -> Option<Dst>

Performs the conversion.
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impl<Src, Dst> LossyInto<Dst> for Src
where Dst: LossyFrom<Src>,

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fn lossy_into(self) -> Dst

Performs the conversion.
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impl<T> OverflowingAs for T

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fn overflowing_as<Dst>(self) -> (Dst, bool)
where T: OverflowingCast<Dst>,

Casts the value.
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impl<Src, Dst> OverflowingCastFrom<Src> for Dst
where Src: OverflowingCast<Dst>,

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fn overflowing_cast_from(src: Src) -> (Dst, bool)

Casts the value.
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impl<P, T> Receiver for P
where P: Deref<Target = T> + ?Sized, T: ?Sized,

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type Target = T

🔬This is a nightly-only experimental API. (arbitrary_self_types)
The target type on which the method may be called.
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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<T> SaturatingAs for T

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fn saturating_as<Dst>(self) -> Dst
where T: SaturatingCast<Dst>,

Casts the value.
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impl<Src, Dst> SaturatingCastFrom<Src> for Dst
where Src: SaturatingCast<Dst>,

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fn saturating_cast_from(src: Src) -> Dst

Casts the value.
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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> ToString for T
where T: Display + ?Sized,

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fn to_string(&self) -> String

Converts the given value to a String. 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> UnwrappedAs for T

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fn unwrapped_as<Dst>(self) -> Dst
where T: UnwrappedCast<Dst>,

Casts the value.
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impl<Src, Dst> UnwrappedCastFrom<Src> for Dst
where Src: UnwrappedCast<Dst>,

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fn unwrapped_cast_from(src: Src) -> Dst

Casts the value.
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impl<V, T> VZip<V> for T
where V: MultiLane<T>,

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fn vzip(self) -> V

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impl<T> WrappingAs for T

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fn wrapping_as<Dst>(self) -> Dst
where T: WrappingCast<Dst>,

Casts the value.
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impl<Src, Dst> WrappingCastFrom<Src> for Dst
where Src: WrappingCast<Dst>,

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fn wrapping_cast_from(src: Src) -> Dst

Casts the value.
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impl<T> MaybeSerDes for T