Struct snarkvm_fields::Fp2

pub struct Fp2<P: Fp2Parameters> {
    pub c0: P::Fp,
    pub c1: P::Fp,
}

Fields

c0: P::Fp

c1: P::Fp

Implementations

impl<P: Fp2Parameters> Fp2<P>

pub fn new(c0: P::Fp, c1: P::Fp) -> Self

pub fn norm(&self) -> P::Fp

Norm of Fp2 over Fp: Norm(a) = a.x^2 - beta * a.y^2

pub fn mul_by_fp(&mut self, element: &P::Fp)

Trait Implementations

impl<P: Fp2Parameters> Add<&'_ &'_ Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the + operator.

fn add(self, other: &&Self) -> Self

Performs the + operation.

impl<'a, P: Fp2Parameters> Add<&'a Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the + operator.

fn add(self, other: &Self) -> Self

Performs the + operation.

impl<'a, P: Fp2Parameters> Add<&'a mut Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the + operator.

fn add(self, other: &'a mut Self) -> Self

Performs the + operation.

impl<P: Fp2Parameters> Add<Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P: Fp2Parameters> AddAssign<&'_ &'_ Fp2<P>> for Fp2<P>

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

Performs the += operation.

impl<'a, P: Fp2Parameters> AddAssign<&'a Fp2<P>> for Fp2<P>

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

Performs the += operation.

impl<'a, P: Fp2Parameters> AddAssign<&'a mut Fp2<P>> for Fp2<P>

fn add_assign(&mut self, other: &'a mut Self)

Performs the += operation.

impl<P: Fp2Parameters> AddAssign<Fp2<P>> for Fp2<P>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: Fp2Parameters> CanonicalDeserialize for Fp2<P>

fn deserialize<R: Read>(reader: &mut R) -> Result<Self, SerializationError>

Reads Self from reader.

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

Reads Self from reader without compression.

impl<P: Fp2Parameters> CanonicalDeserializeWithFlags for Fp2<P>

fn deserialize_with_flags<R: Read, F: Flags>(
    reader: &mut R
) -> Result<(Self, F), SerializationError>

Reads Self and Flags from reader. Returns empty flags by default.

impl<P: Fp2Parameters> CanonicalSerialize for Fp2<P>

fn serialize<W: Write>(&self, writer: &mut W) -> Result<(), SerializationError>

Serializes self into writer.

fn serialized_size(&self) -> usize

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

Serializes self into writer without compression.

fn uncompressed_size(&self) -> usize

impl<P: Fp2Parameters> CanonicalSerializeWithFlags for Fp2<P>

fn serialize_with_flags<W: Write, F: Flags>(
    &self,
    writer: &mut W,
    flags: F
) -> Result<(), SerializationError>

Serializes self and flags into writer.

impl<P: Fp2Parameters> Clone for Fp2<P> where
    P: Fp2Parameters, 

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P: Fp2Parameters> ConstantSerializedSize for Fp2<P>

const SERIALIZED_SIZE: usize

const UNCOMPRESSED_SIZE: usize

impl<P: Fp2Parameters> Debug for Fp2<P> where
    P: Fp2Parameters, 

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

Formats the value using the given formatter.

impl<P: Fp2Parameters> Default for Fp2<P> where
    P: Fp2Parameters, 

fn default() -> Self

Returns the “default value” for a type.

impl<'de, P: Fp2Parameters> Deserialize<'de> for Fp2<P> where
    P::Fp: Deserialize<'de>,
    P::Fp: Deserialize<'de>, 

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where
    __D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<P: Fp2Parameters> Display for Fp2<P>

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

Formats the value using the given formatter.

impl<P: Fp2Parameters> Distribution<Fp2<P>> for Standard

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp2<P>

Generate a random value of T, using rng as the source of randomness.

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

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S> where
    F: Fn(T) -> S, 

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<P: Fp2Parameters> Div<&'_ &'_ Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the / operator.

fn div(self, other: &&Self) -> Self

Performs the / operation.

impl<'a, P: Fp2Parameters> Div<&'a Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the / operator.

fn div(self, other: &Self) -> Self

Performs the / operation.

impl<'a, P: Fp2Parameters> Div<&'a mut Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the / operator.

fn div(self, other: &'a mut Self) -> Self

Performs the / operation.

impl<P: Fp2Parameters> Div<Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the / operator.

fn div(self, other: Self) -> Self

Performs the / operation.

impl<P: Fp2Parameters> DivAssign<&'_ &'_ Fp2<P>> for Fp2<P>

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

Performs the /= operation.

impl<'a, P: Fp2Parameters> DivAssign<&'a Fp2<P>> for Fp2<P>

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

Performs the /= operation.

impl<'a, P: Fp2Parameters> DivAssign<&'a mut Fp2<P>> for Fp2<P>

fn div_assign(&mut self, other: &'a mut Self)

Performs the /= operation.

impl<P: Fp2Parameters> DivAssign<Fp2<P>> for Fp2<P>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<P: Fp2Parameters> Field for Fp2<P>

fn characteristic<'a>() -> &'a [u64]

Returns the characteristic of the field.

fn double(&self) -> Self

Returns self + self.

fn double_in_place(&mut self)

Doubles self in place.

fn square(&self) -> Self

Returns self * self.

fn from_random_bytes_with_flags<F: Flags>(bytes: &[u8]) -> Option<(Self, F)>

Returns a field element with an extra sign bit used for group parsing if the set of bytes forms a valid field element, otherwise returns None. This function is primarily intended for sampling random field elements from a hash-function or RNG output.

fn from_random_bytes(bytes: &[u8]) -> Option<Self>

Returns a field element if the set of bytes forms a valid field element, otherwise returns None. This function is primarily intended for sampling random field elements from a hash-function or RNG output.

fn square_in_place(&mut self) -> &mut Self

Squares self in place.

fn inverse(&self) -> Option<Self>

Computes the multiplicative inverse of self if self is nonzero.

fn inverse_in_place(&mut self) -> Option<&mut Self>

Sets self to self’s inverse if it exists. Otherwise it is a no-op.

fn frobenius_map(&mut self, power: usize)

Exponentiates this element by a power of the base prime modulus via the Frobenius automorphism.

fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self

Exponentiates this element by a number represented with u64 limbs, least significant limb first.

impl<P: Fp2Parameters> From<u128> for Fp2<P>

fn from(other: u128) -> Self

Performs the conversion.

impl<P: Fp2Parameters> From<u16> for Fp2<P>

fn from(other: u16) -> Self

Performs the conversion.

impl<P: Fp2Parameters> From<u32> for Fp2<P>

fn from(other: u32) -> Self

Performs the conversion.

impl<P: Fp2Parameters> From<u64> for Fp2<P>

fn from(other: u64) -> Self

Performs the conversion.

impl<P: Fp2Parameters> From<u8> for Fp2<P>

fn from(other: u8) -> Self

Performs the conversion.

impl<P: Fp2Parameters> FromBytes for Fp2<P>

fn read_le<R: Read>(reader: R) -> IoResult<Self>

Reads Self from reader as little-endian bytes.

fn from_bytes_le(bytes: &[u8]) -> Result<Self, Error>

Returns Self from a byte array in little-endian order.

impl<P: Fp2Parameters> Hash for Fp2<P> where
    P: Fp2Parameters, 

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

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given Hasher.

impl<P: Fp2Parameters> Mul<&'_ &'_ Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the * operator.

fn mul(self, other: &&Self) -> Self

Performs the * operation.

impl<'a, P: Fp2Parameters> Mul<&'a Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the * operator.

fn mul(self, other: &Self) -> Self

Performs the * operation.

impl<'a, P: Fp2Parameters> Mul<&'a mut Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the * operator.

fn mul(self, other: &'a mut Self) -> Self

Performs the * operation.

impl<P: Fp2Parameters> Mul<Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the * operator.

fn mul(self, other: Self) -> Self

Performs the * operation.

impl<P: Fp2Parameters> MulAssign<&'_ &'_ Fp2<P>> for Fp2<P>

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

Performs the *= operation.

impl<'a, P: Fp2Parameters> MulAssign<&'a Fp2<P>> for Fp2<P>

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

Performs the *= operation.

impl<'a, P: Fp2Parameters> MulAssign<&'a mut Fp2<P>> for Fp2<P>

fn mul_assign(&mut self, other: &'a mut Self)

Performs the *= operation.

impl<P: Fp2Parameters> MulAssign<Fp2<P>> for Fp2<P>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<P: Fp2Parameters> Neg for Fp2<P>

type Output = Self

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<P: Fp2Parameters> One for Fp2<P>

fn one() -> Self

fn is_one(&self) -> bool

impl<P: Fp2Parameters> Ord for Fp2<P>

Fp2 elements are ordered lexicographically.

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

Restrict a value to a certain interval.

impl<P: Fp2Parameters> PartialEq<Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

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

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=.

impl<P: Fp2Parameters> PartialOrd<Fp2<P>> for Fp2<P>

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

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<'a, P: Fp2Parameters> Product<&'a Fp2<P>> for Fp2<P>

fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<P: Fp2Parameters> Product<Fp2<P>> for Fp2<P>

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<P: Fp2Parameters> Serialize for Fp2<P> where
    P::Fp: Serialize,
    P::Fp: Serialize, 

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where
    __S: Serializer, 

Serialize this value into the given Serde serializer.

impl<'a, P: Fp2Parameters> SquareRootField for Fp2<P> where
    P::Fp: SquareRootField, 

fn legendre(&self) -> LegendreSymbol

Returns the Legendre symbol.

fn sqrt(&self) -> Option<Self>

Returns the square root of self, if it exists.

fn sqrt_in_place(&mut self) -> Option<&mut Self>

Sets self to be the square root of self, if it exists.

impl<P: Fp2Parameters> Sub<&'_ &'_ Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the - operator.

fn sub(self, other: &&Self) -> Self

Performs the - operation.

impl<'a, P: Fp2Parameters> Sub<&'a Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the - operator.

fn sub(self, other: &Self) -> Self

Performs the - operation.

impl<'a, P: Fp2Parameters> Sub<&'a mut Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the - operator.

fn sub(self, other: &'a mut Self) -> Self

Performs the - operation.

impl<P: Fp2Parameters> Sub<Fp2<P>> for Fp2<P>

type Output = Self

The resulting type after applying the - operator.

fn sub(self, other: Self) -> Self

Performs the - operation.

impl<P: Fp2Parameters> SubAssign<&'_ &'_ Fp2<P>> for Fp2<P>

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

Performs the -= operation.

impl<'a, P: Fp2Parameters> SubAssign<&'a Fp2<P>> for Fp2<P>

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

Performs the -= operation.

impl<'a, P: Fp2Parameters> SubAssign<&'a mut Fp2<P>> for Fp2<P>

fn sub_assign(&mut self, other: &'a mut Self)

Performs the -= operation.

impl<P: Fp2Parameters> SubAssign<Fp2<P>> for Fp2<P>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<'a, P: Fp2Parameters> Sum<&'a Fp2<P>> for Fp2<P>

fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<P: Fp2Parameters> Sum<Fp2<P>> for Fp2<P>

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<P: Fp2Parameters> ToBytes for Fp2<P>

fn write_le<W: Write>(&self, writer: W) -> IoResult<()>

Writes self into writer as little-endian bytes.

fn to_bytes_le(&self) -> Result<Vec<u8, Global>, Error>

Returns self as a byte array in little-endian order.

impl<P: Fp2Parameters> ToConstraintField<<P as Fp2Parameters>::Fp> for Fp2<P>

fn to_field_elements(&self) -> Result<Vec<P::Fp>, ConstraintFieldError>

impl<P: Fp2Parameters> Zero for Fp2<P>

fn zero() -> Self

fn is_zero(&self) -> bool

impl<P: Fp2Parameters> Copy for Fp2<P> where
    P: Fp2Parameters, 

impl<P: Fp2Parameters> Eq for Fp2<P> where
    P: Fp2Parameters,