pub struct Affine<P: TECurveConfig> {
    pub x: P::BaseField,
    pub y: P::BaseField,
}
Expand description

Affine coordinates for a point on a twisted Edwards curve, over the base field P::BaseField.

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§x: P::BaseField

X coordinate of the point represented as a field element

§y: P::BaseField

Y coordinate of the point represented as a field element

Implementations§

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impl<P: TECurveConfig> Affine<P>

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pub const fn new_unchecked(x: P::BaseField, y: P::BaseField) -> Self

Construct a new group element without checking whether the coordinates specify a point in the subgroup.

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pub fn new(x: P::BaseField, y: P::BaseField) -> Self

Construct a new group element in a way while enforcing that points are in the prime-order subgroup.

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pub const fn zero() -> Self

Construct the identity of the group

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pub fn is_zero(&self) -> bool

Is this point the identity?

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pub fn get_point_from_y_unchecked( y: P::BaseField, greatest: bool ) -> Option<Self>

Attempts to construct an affine point given an y-coordinate. The point is not guaranteed to be in the prime order subgroup.

If and only if greatest is set will the lexicographically largest x-coordinate be selected.

a * X^2 + Y^2 = 1 + d * X^2 * Y^2 a * X^2 - d * X^2 * Y^2 = 1 - Y^2 X^2 * (a - d * Y^2) = 1 - Y^2 X^2 = (1 - Y^2) / (a - d * Y^2)

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pub fn get_xs_from_y_unchecked( y: P::BaseField ) -> Option<(P::BaseField, P::BaseField)>

Attempts to recover the x-coordinate given an y-coordinate. The resulting point is not guaranteed to be in the prime order subgroup.

If and only if greatest is set will the lexicographically largest x-coordinate be selected.

a * X^2 + Y^2 = 1 + d * X^2 * Y^2 a * X^2 - d * X^2 * Y^2 = 1 - Y^2 X^2 * (a - d * Y^2) = 1 - Y^2 X^2 = (1 - Y^2) / (a - d * Y^2)

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pub fn is_on_curve(&self) -> bool

Checks that the current point is on the elliptic curve.

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impl<P: TECurveConfig> Affine<P>

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pub fn is_in_correct_subgroup_assuming_on_curve(&self) -> bool

Checks if self is in the subgroup having order equaling that of P::ScalarField given it is on the curve.

Trait Implementations§

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impl<'a, P: TECurveConfig> Add<&'a Projective<P>> for Affine<P>

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type Output = Projective<P>

The resulting type after applying the + operator.
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fn add(self, other: &'a Projective<P>) -> Projective<P>

Performs the + operation. Read more
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impl<P: TECurveConfig> Add<Projective<P>> for Affine<P>

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type Output = Projective<P>

The resulting type after applying the + operator.
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fn add(self, other: Projective<P>) -> Projective<P>

Performs the + operation. Read more
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impl<P: TECurveConfig, T: Borrow<Self>> Add<T> for Affine<P>

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type Output = Projective<P>

The resulting type after applying the + operator.
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fn add(self, other: T) -> Self::Output

Performs the + operation. Read more
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impl<P: TECurveConfig> AffineRepr for Affine<P>

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fn mul_by_cofactor_to_group(&self) -> Self::Group

Multiplies this element by the cofactor and output the resulting projective element.

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fn clear_cofactor(&self) -> Self

Performs cofactor clearing. The default method is simply to multiply by the cofactor. Some curves can implement a more efficient algorithm.

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type Config = P

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type BaseField = <P as CurveConfig>::BaseField

The finite field over which this curve is defined.
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type ScalarField = <P as CurveConfig>::ScalarField

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type Group = Projective<P>

The projective representation of points on this curve.
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fn xy(&self) -> Option<(&Self::BaseField, &Self::BaseField)>

Returns the x and y coordinates of this affine point.
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fn generator() -> Self

Returns a fixed generator of unknown exponent.
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fn zero() -> Self

Returns the point at infinity.
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fn from_random_bytes(bytes: &[u8]) -> Option<Self>

Returns a group element if the set of bytes forms a valid group element, otherwise returns None. This function is primarily intended for sampling random group elements from a hash-function or RNG output.
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fn mul_bigint(&self, by: impl AsRef<[u64]>) -> Self::Group

Performs scalar multiplication of this element with mixed addition.
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fn x(&self) -> Option<&Self::BaseField>

Returns the x coordinate of this affine point.
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fn y(&self) -> Option<&Self::BaseField>

Returns the y coordinate of this affine point.
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fn is_zero(&self) -> bool

Is self the point at infinity?
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fn into_group(self) -> Self::Group

Converts self into the projective representation.
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fn mul_by_cofactor(&self) -> Self

Multiplies this element by the cofactor.
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fn mul_by_cofactor_inv(&self) -> Self

Multiplies this element by the inverse of the cofactor in Self::ScalarField.
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impl<P: TECurveConfig> CanonicalDeserialize for Affine<P>

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fn deserialize_with_mode<R: Read>( reader: R, compress: Compress, validate: Validate ) -> Result<Self, SerializationError>

The general deserialize method that takes in customization flags.
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fn deserialize_compressed<R>(reader: R) -> Result<Self, SerializationError>where R: Read,

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fn deserialize_compressed_unchecked<R>( reader: R ) -> Result<Self, SerializationError>where R: Read,

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fn deserialize_uncompressed<R>(reader: R) -> Result<Self, SerializationError>where R: Read,

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fn deserialize_uncompressed_unchecked<R>( reader: R ) -> Result<Self, SerializationError>where R: Read,

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impl<P: TECurveConfig> CanonicalSerialize for Affine<P>

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fn serialize_with_mode<W: Write>( &self, writer: W, compress: Compress ) -> Result<(), SerializationError>

The general serialize method that takes in customization flags.
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fn serialized_size(&self, compress: Compress) -> usize

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fn serialize_compressed<W>(&self, writer: W) -> Result<(), SerializationError>where W: Write,

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fn compressed_size(&self) -> usize

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fn serialize_uncompressed<W>(&self, writer: W) -> Result<(), SerializationError>where W: Write,

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fn uncompressed_size(&self) -> usize

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impl<P> Clone for Affine<P>where P: TECurveConfig,

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fn clone(&self) -> Self

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<P: TECurveConfig> Debug for Affine<P>

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

Formats the value using the given formatter. Read more
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impl<P: TECurveConfig> Default for Affine<P>

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fn default() -> Self

Returns the “default value” for a type. Read more
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impl<P: TECurveConfig> Display for Affine<P>

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

Formats the value using the given formatter. Read more
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impl<P: TECurveConfig> Distribution<Affine<P>> for Standard

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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Affine<P>

Generates a uniformly random instance of the curve.

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fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness. Read more
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fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F Read more
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impl<P: TECurveConfig> From<Affine<P>> for Projective<P>

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fn from(p: Affine<P>) -> Projective<P>

Converts to this type from the input type.
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impl<P: TECurveConfig> From<Projective<P>> for Affine<P>

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fn from(p: Projective<P>) -> Affine<P>

Converts to this type from the input type.
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impl<P> Hash for Affine<P>where P: TECurveConfig,

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fn hash<__HP>(&self, __state: &mut __HP)where __HP: Hasher,

Feeds this value into the given Hasher. Read more
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fn hash_slice<H>(data: &[Self], state: &mut H)where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher. Read more
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impl<P: TECurveConfig, T: Borrow<P::ScalarField>> Mul<T> for Affine<P>

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type Output = Projective<P>

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

Performs the * operation. Read more
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impl<P: TECurveConfig> Neg for Affine<P>

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type Output = Affine<P>

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

Performs the unary - operation. Read more
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impl<P> PartialEq<Affine<P>> for Affine<P>where P: TECurveConfig,

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fn eq(&self, other: &Self) -> 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<P: TECurveConfig> PartialEq<Affine<P>> for Projective<P>

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fn eq(&self, other: &Affine<P>) -> 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<P: TECurveConfig> PartialEq<Projective<P>> for Affine<P>

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fn eq(&self, other: &Projective<P>) -> 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<P: TECurveConfig, T: Borrow<Self>> Sub<T> for Affine<P>

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type Output = Projective<P>

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

Performs the - operation. Read more
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impl<M: TECurveConfig, ConstraintF: Field> ToConstraintField<ConstraintF> for Affine<M>where M::BaseField: ToConstraintField<ConstraintF>,

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fn to_field_elements(&self) -> Option<Vec<ConstraintF>>

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impl<P: TECurveConfig> Valid for Affine<P>

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fn check(&self) -> Result<(), SerializationError>

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fn batch_check<'a>( batch: impl Iterator<Item = &'a Self> + Send ) -> Result<(), SerializationError>where Self: 'a,

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impl<P: TECurveConfig> Zeroize for Affine<P>

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fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.
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impl<P> Copy for Affine<P>where P: TECurveConfig,

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impl<P> Eq for Affine<P>where P: TECurveConfig,

Auto Trait Implementations§

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impl<P> RefUnwindSafe for Affine<P>where <P as CurveConfig>::BaseField: RefUnwindSafe,

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impl<P> Send for Affine<P>

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impl<P> Sync for Affine<P>

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impl<P> Unpin for Affine<P>where <P as CurveConfig>::BaseField: Unpin,

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impl<P> UnwindSafe for Affine<P>where <P as CurveConfig>::BaseField: UnwindSafe,

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impl<T> Any for Twhere 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 Twhere 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 Twhere T: ?Sized,

const: unstable · source§

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

Mutably borrows from an owned value. Read more
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impl<T> CanonicalSerializeHashExt for Twhere T: CanonicalSerialize,

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fn hash<H>(&self) -> GenericArray<u8, <H as OutputSizeUser>::OutputSize>where H: Digest,

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fn hash_uncompressed<H>( &self ) -> GenericArray<u8, <H as OutputSizeUser>::OutputSize>where H: Digest,

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impl<Q, K> Equivalent<K> for Qwhere Q: Eq + ?Sized, K: Borrow<Q> + ?Sized,

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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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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 Twhere 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> Same<T> for T

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type Output = T

Should always be Self
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impl<T> ToOwned for Twhere 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 Twhere T: Display + ?Sized,

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default fn to_string(&self) -> String

Converts the given value to a String. Read more
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impl<T, U> TryFrom<U> for Twhere 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 Twhere 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> UniformRand for Twhere Standard: Distribution<T>,

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fn rand<R>(rng: &mut R) -> Twhere R: Rng + ?Sized,

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impl<V, T> VZip<V> for Twhere V: MultiLane<T>,

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fn vzip(self) -> V